diff --git a/examples/Hybrid_City10000.cpp b/examples/Hybrid_City10000.cpp
index ca7f03e74..b1afff95a 100644
--- a/examples/Hybrid_City10000.cpp
+++ b/examples/Hybrid_City10000.cpp
@@ -31,11 +31,12 @@
 
 #include <boost/algorithm/string/classification.hpp>
 #include <boost/algorithm/string/split.hpp>
+#include <cstdlib>
 #include <fstream>
+#include <iostream>
 #include <string>
 #include <vector>
 
-using namespace std;
 using namespace gtsam;
 using namespace boost::algorithm;
 
@@ -43,19 +44,30 @@ using symbol_shorthand::L;
 using symbol_shorthand::M;
 using symbol_shorthand::X;
 
-const size_t kMaxLoopCount = 2000;  // Example default value
-const size_t kMaxNrHypotheses = 10;
-
 auto kOpenLoopModel = noiseModel::Diagonal::Sigmas(Vector3::Ones() * 10);
+const double kOpenLoopConstant = kOpenLoopModel->negLogConstant();
 
 auto kPriorNoiseModel = noiseModel::Diagonal::Sigmas(
     (Vector(3) << 0.0001, 0.0001, 0.0001).finished());
 
 auto kPoseNoiseModel = noiseModel::Diagonal::Sigmas(
     (Vector(3) << 1.0 / 30.0, 1.0 / 30.0, 1.0 / 100.0).finished());
+const double kPoseNoiseConstant = kPoseNoiseModel->negLogConstant();
 
 // Experiment Class
 class Experiment {
+ public:
+  // Parameters with default values
+  size_t maxLoopCount = 3000;
+
+  // 3000: {1: 62s, 2: 21s, 3: 20s, 4: 31s, 5: 39s} No DT optimizations
+  // 3000: {1: 65s, 2: 20s, 3: 16s, 4: 21s, 5: 28s} With DT optimizations
+  // 3000: {1: 59s, 2: 19s, 3: 18s, 4: 26s, 5: 33s} With DT optimizations +
+  // merge
+  size_t updateFrequency = 3;
+
+  size_t maxNrHypotheses = 10;
+
  private:
   std::string filename_;
   HybridSmoother smoother_;
@@ -72,7 +84,7 @@ class Experiment {
    */
   void writeResult(const Values& result, size_t numPoses,
                    const std::string& filename = "Hybrid_city10000.txt") {
-    ofstream outfile;
+    std::ofstream outfile;
     outfile.open(filename);
 
     for (size_t i = 0; i < numPoses; ++i) {
@@ -98,9 +110,8 @@ class Experiment {
     auto f1 = std::make_shared<BetweenFactor<Pose2>>(
         X(keyS), X(keyT), measurement, kPoseNoiseModel);
 
-    std::vector<NonlinearFactorValuePair> factors{
-        {f0, kOpenLoopModel->negLogConstant()},
-        {f1, kPoseNoiseModel->negLogConstant()}};
+    std::vector<NonlinearFactorValuePair> factors{{f0, kOpenLoopConstant},
+                                                  {f1, kPoseNoiseConstant}};
     HybridNonlinearFactor mixtureFactor(l, factors);
     return mixtureFactor;
   }
@@ -114,9 +125,8 @@ class Experiment {
     auto f1 = std::make_shared<BetweenFactor<Pose2>>(
         X(keyS), X(keyT), poseArray[1], kPoseNoiseModel);
 
-    std::vector<NonlinearFactorValuePair> factors{
-        {f0, kPoseNoiseModel->negLogConstant()},
-        {f1, kPoseNoiseModel->negLogConstant()}};
+    std::vector<NonlinearFactorValuePair> factors{{f0, kPoseNoiseConstant},
+                                                  {f1, kPoseNoiseConstant}};
     HybridNonlinearFactor mixtureFactor(m, factors);
     return mixtureFactor;
   }
@@ -124,9 +134,9 @@ class Experiment {
   /// @brief Perform smoother update and optimize the graph.
   void smootherUpdate(HybridSmoother& smoother,
                       HybridNonlinearFactorGraph& graph, const Values& initial,
-                      size_t kMaxNrHypotheses, Values* result) {
+                      size_t maxNrHypotheses, Values* result) {
     HybridGaussianFactorGraph linearized = *graph.linearize(initial);
-    smoother.update(linearized, kMaxNrHypotheses);
+    smoother.update(linearized, maxNrHypotheses);
     // throw if x0 not in hybridBayesNet_:
     const KeySet& keys = smoother.hybridBayesNet().keys();
     if (keys.find(X(0)) == keys.end()) {
@@ -143,11 +153,11 @@ class Experiment {
       : filename_(filename), smoother_(0.99) {}
 
   /// @brief Run the main experiment with a given maxLoopCount.
-  void run(size_t maxLoopCount) {
+  void run() {
     // Prepare reading
-    ifstream in(filename_);
+    std::ifstream in(filename_);
     if (!in.is_open()) {
-      cerr << "Failed to open file: " << filename_ << endl;
+      std::cerr << "Failed to open file: " << filename_ << std::endl;
       return;
     }
 
@@ -168,11 +178,14 @@ class Experiment {
 
     // Initial update
     clock_t beforeUpdate = clock();
-    smootherUpdate(smoother_, graph_, initial_, kMaxNrHypotheses, &result_);
+    smootherUpdate(smoother_, graph_, initial_, maxNrHypotheses, &result_);
     clock_t afterUpdate = clock();
     std::vector<std::pair<size_t, double>> smootherUpdateTimes;
     smootherUpdateTimes.push_back({index, afterUpdate - beforeUpdate});
 
+    // Flag to decide whether to run smoother update
+    size_t numberOfHybridFactors = 0;
+
     // Start main loop
     size_t keyS = 0, keyT = 0;
     clock_t startTime = clock();
@@ -193,9 +206,6 @@ class Experiment {
         poseArray[i] = Pose2(x, y, rad);
       }
 
-      // Flag to decide whether to run smoother update
-      bool doSmootherUpdate = false;
-
       // Take the first one as the initial estimate
       Pose2 odomPose = poseArray[0];
       if (keyS == keyT - 1) {
@@ -207,8 +217,8 @@ class Experiment {
               hybridOdometryFactor(numMeasurements, keyS, keyT, m, poseArray);
           graph_.push_back(mixtureFactor);
           discreteCount++;
-          doSmootherUpdate = true;
-          // std::cout << "mixtureFactor: " << keyS << " " << keyT << std::endl;
+          numberOfHybridFactors += 1;
+          std::cout << "mixtureFactor: " << keyS << " " << keyT << std::endl;
         } else {
           graph_.add(BetweenFactor<Pose2>(X(keyS), X(keyT), odomPose,
                                           kPoseNoiseModel));
@@ -220,20 +230,22 @@ class Experiment {
         HybridNonlinearFactor loopFactor =
             hybridLoopClosureFactor(loopCount, keyS, keyT, odomPose);
         // print loop closure event keys:
-        // std::cout << "Loop closure: " << keyS << " " << keyT << std::endl;
+        std::cout << "Loop closure: " << keyS << " " << keyT << std::endl;
         graph_.add(loopFactor);
-        doSmootherUpdate = true;
+        numberOfHybridFactors += 1;
         loopCount++;
       }
 
-      if (doSmootherUpdate) {
+      if (numberOfHybridFactors >= updateFrequency) {
+        // print the keys involved in the smoother update
+        std::cout << "Smoother update: " << graph_.size() << std::endl;
         gttic_(SmootherUpdate);
         beforeUpdate = clock();
-        smootherUpdate(smoother_, graph_, initial_, kMaxNrHypotheses, &result_);
+        smootherUpdate(smoother_, graph_, initial_, maxNrHypotheses, &result_);
         afterUpdate = clock();
         smootherUpdateTimes.push_back({index, afterUpdate - beforeUpdate});
         gttoc_(SmootherUpdate);
-        doSmootherUpdate = false;
+        numberOfHybridFactors = 0;
       }
 
       // Record timing for odometry edges only
@@ -259,7 +271,7 @@ class Experiment {
 
     // Final update
     beforeUpdate = clock();
-    smootherUpdate(smoother_, graph_, initial_, kMaxNrHypotheses, &result_);
+    smootherUpdate(smoother_, graph_, initial_, maxNrHypotheses, &result_);
     afterUpdate = clock();
     smootherUpdateTimes.push_back({index, afterUpdate - beforeUpdate});
 
@@ -289,7 +301,7 @@ class Experiment {
     //  }
 
     // Write timing info to file
-    ofstream outfileTime;
+    std::ofstream outfileTime;
     std::string timeFileName = "Hybrid_City10000_time.txt";
     outfileTime.open(timeFileName);
     for (auto accTime : timeList) {
@@ -301,15 +313,47 @@ class Experiment {
 };
 
 /* ************************************************************************* */
-int main() {
+// Function to parse command-line arguments
+void parseArguments(int argc, char* argv[], size_t& maxLoopCount,
+                    size_t& updateFrequency, size_t& maxNrHypotheses) {
+  for (int i = 1; i < argc; ++i) {
+    std::string arg = argv[i];
+    if (arg == "--max-loop-count" && i + 1 < argc) {
+      maxLoopCount = std::stoul(argv[++i]);
+    } else if (arg == "--update-frequency" && i + 1 < argc) {
+      updateFrequency = std::stoul(argv[++i]);
+    } else if (arg == "--max-nr-hypotheses" && i + 1 < argc) {
+      maxNrHypotheses = std::stoul(argv[++i]);
+    } else if (arg == "--help") {
+      std::cout << "Usage: " << argv[0] << " [options]\n"
+                << "Options:\n"
+                << "  --max-loop-count <value>       Set the maximum loop "
+                   "count (default: 3000)\n"
+                << "  --update-frequency <value>     Set the update frequency "
+                   "(default: 3)\n"
+                << "  --max-nr-hypotheses <value>    Set the maximum number of "
+                   "hypotheses (default: 10)\n"
+                << "  --help                         Show this help message\n";
+      std::exit(0);
+    }
+  }
+}
+
+/* ************************************************************************* */
+// Main function
+int main(int argc, char* argv[]) {
   Experiment experiment(findExampleDataFile("T1_city10000_04.txt"));
   // Experiment experiment("../data/mh_T1_city10000_04.txt"); //Type #1 only
   // Experiment experiment("../data/mh_T3b_city10000_10.txt"); //Type #3 only
   // Experiment experiment("../data/mh_T1_T3_city10000_04.txt"); //Type #1 +
   // Type #3
 
+  // Parse command-line arguments
+  parseArguments(argc, argv, experiment.maxLoopCount,
+                 experiment.updateFrequency, experiment.maxNrHypotheses);
+
   // Run the experiment
-  experiment.run(kMaxLoopCount);
+  experiment.run();
 
   return 0;
-}
+}
\ No newline at end of file
diff --git a/gtsam/discrete/DecisionTree-inl.h b/gtsam/discrete/DecisionTree-inl.h
index efc19d9ee..89091c78b 100644
--- a/gtsam/discrete/DecisionTree-inl.h
+++ b/gtsam/discrete/DecisionTree-inl.h
@@ -74,8 +74,8 @@ namespace gtsam {
 
     /// equality up to tolerance
     bool equals(const Node& q, const CompareFunc& compare) const override {
-      const Leaf* other = dynamic_cast<const Leaf*>(&q);
-      if (!other) return false;
+      if (!q.isLeaf()) return false;
+      const Leaf* other = static_cast<const Leaf*>(&q);
       return compare(this->constant_, other->constant_);
     }
 
@@ -202,36 +202,39 @@ namespace gtsam {
      * @param node The root node of the decision tree.
      * @return NodePtr
      */
+    #ifdef GTSAM_DT_MERGING
+
     static NodePtr Unique(const NodePtr& node) {
-      if (auto choice = std::dynamic_pointer_cast<const Choice>(node)) {
-        // Choice node, we recurse!
-        // Make non-const copy so we can update
-        auto f = std::make_shared<Choice>(choice->label(), choice->nrChoices());
+      if (node->isLeaf()) return node;  // Leaf node, return as is
 
-        // Iterate over all the branches
-        for (size_t i = 0; i < choice->nrChoices(); i++) {
-          auto branch = choice->branches_[i];
-          f->push_back(Unique(branch));
-        }
+      auto choice = std::static_pointer_cast<const Choice>(node);
+      // Choice node, we recurse!
+      // Make non-const copy so we can update
+      auto f = std::make_shared<Choice>(choice->label(), choice->nrChoices());
 
-#ifdef GTSAM_DT_MERGING
-        // If all the branches are the same, we can merge them into one
-        if (f->allSame_) {
-          assert(f->branches().size() > 0);
-          NodePtr f0 = f->branches_[0];
-
-          NodePtr newLeaf(
-              new Leaf(std::dynamic_pointer_cast<const Leaf>(f0)->constant()));
-          return newLeaf;
-        }
-#endif
-        return f;
-      } else {
-        // Leaf node, return as is
-        return node;
+      // Iterate over all the branches
+      for (const auto& branch : choice->branches_) {
+        f->push_back(Unique(branch));
       }
+
+      // If all the branches are the same, we can merge them into one
+      if (f->allSame_) {
+        assert(f->branches().size() > 0);
+        auto f0 = std::static_pointer_cast<const Leaf>(f->branches_[0]);
+        return std::make_shared<Leaf>(f0->constant());
+      }
+
+      return f;
     }
 
+    #else
+
+    static NodePtr Unique(const NodePtr& node) {
+      // No-op when GTSAM_DT_MERGING is not defined
+      return node;
+    }
+
+    #endif
     bool isLeaf() const override { return false; }
 
     /// Constructor, given choice label and mandatory expected branch count.
@@ -322,9 +325,9 @@ namespace gtsam {
         const NodePtr& branch = branches_[i];
 
         // Check if zero
-        if (!showZero) {
-          const Leaf* leaf = dynamic_cast<const Leaf*>(branch.get());
-          if (leaf && valueFormatter(leaf->constant()).compare("0")) continue;
+        if (!showZero && branch->isLeaf()) {
+            auto leaf = std::static_pointer_cast<const Leaf>(branch);
+          if (valueFormatter(leaf->constant()).compare("0")) continue;
         }
 
         os << "\"" << this->id() << "\" -> \"" << branch->id() << "\"";
@@ -346,8 +349,8 @@ namespace gtsam {
 
     /// equality
     bool equals(const Node& q, const CompareFunc& compare) const override {
-      const Choice* other = dynamic_cast<const Choice*>(&q);
-      if (!other) return false;
+      if (q.isLeaf()) return false;
+      const Choice* other = static_cast<const Choice*>(&q);
       if (this->label_ != other->label_) return false;
       if (branches_.size() != other->branches_.size()) return false;
       // we don't care about shared pointers being equal here
@@ -570,11 +573,13 @@ namespace gtsam {
       struct ApplyUnary {
         const Unary& op;
         void operator()(typename DecisionTree<L, Y>::NodePtr& node) const {
-          if (auto leaf = std::dynamic_pointer_cast<Leaf>(node)) {
+          if (node->isLeaf()) {
             // Apply the unary operation to the leaf's constant value
+            auto leaf = std::static_pointer_cast<Leaf>(node);
             leaf->constant_ = op(leaf->constant_);
-          } else if (auto choice = std::dynamic_pointer_cast<Choice>(node)) {
+          } else {
             // Recurse into the choice branches
+            auto choice = std::static_pointer_cast<Choice>(node);
             for (NodePtr& branch : choice->branches()) {
               (*this)(branch);
             }
@@ -622,8 +627,7 @@ namespace gtsam {
     for (Iterator it = begin; it != end; it++) {
       if (it->root_->isLeaf())
         continue;
-      std::shared_ptr<const Choice> c =
-          std::dynamic_pointer_cast<const Choice>(it->root_);
+      auto c = std::static_pointer_cast<const Choice>(it->root_);
       if (!highestLabel || c->label() > *highestLabel) {
         highestLabel = c->label();
         nrChoices = c->nrChoices();
@@ -729,11 +733,7 @@ namespace gtsam {
   typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::create(
       It begin, It end, ValueIt beginY, ValueIt endY) {
     auto node = build(begin, end, beginY, endY);
-    if (auto choice = std::dynamic_pointer_cast<Choice>(node)) {
-      return Choice::Unique(choice);
-    } else {
-      return node;
-    }
+    return Choice::Unique(node);
   }
 
   /****************************************************************************/
@@ -742,18 +742,17 @@ namespace gtsam {
   typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::convertFrom(
       const typename DecisionTree<L, X>::NodePtr& f,
       std::function<Y(const X&)> Y_of_X) {
+    using LXLeaf = typename DecisionTree<L, X>::Leaf;
+    using LXChoice = typename DecisionTree<L, X>::Choice;
 
     // If leaf, apply unary conversion "op" and create a unique leaf.
-    using LXLeaf = typename DecisionTree<L, X>::Leaf;
-    if (auto leaf = std::dynamic_pointer_cast<LXLeaf>(f)) {
+    if (f->isLeaf()) {
+      auto leaf = std::static_pointer_cast<LXLeaf>(f);
       return NodePtr(new Leaf(Y_of_X(leaf->constant())));
     }
 
-    // Check if Choice
-    using LXChoice = typename DecisionTree<L, X>::Choice;
-    auto choice = std::dynamic_pointer_cast<const LXChoice>(f);
-    if (!choice) throw std::invalid_argument(
-        "DecisionTree::convertFrom: Invalid NodePtr");
+    // Now a Choice!
+    auto choice = std::static_pointer_cast<const LXChoice>(f);
 
     // Create a new Choice node with the same label
     auto newChoice = std::make_shared<Choice>(choice->label(), choice->nrChoices());
@@ -773,18 +772,17 @@ namespace gtsam {
       const typename DecisionTree<M, X>::NodePtr& f,
       std::function<L(const M&)> L_of_M, std::function<Y(const X&)> Y_of_X) {
     using LY = DecisionTree<L, Y>;
+    using MXLeaf = typename DecisionTree<M, X>::Leaf;
+    using MXChoice = typename DecisionTree<M, X>::Choice;
 
     // If leaf, apply unary conversion "op" and create a unique leaf.
-    using MXLeaf = typename DecisionTree<M, X>::Leaf;
-    if (auto leaf = std::dynamic_pointer_cast<const MXLeaf>(f)) {
+    if (f->isLeaf()) {
+      auto leaf = std::static_pointer_cast<const MXLeaf>(f);
       return NodePtr(new Leaf(Y_of_X(leaf->constant())));
     }
 
-    // Check if Choice
-    using MXChoice = typename DecisionTree<M, X>::Choice;
-    auto choice = std::dynamic_pointer_cast<const MXChoice>(f);
-    if (!choice)
-      throw std::invalid_argument("DecisionTree::convertFrom: Invalid NodePtr");
+    // Now is Choice!
+    auto choice = std::static_pointer_cast<const MXChoice>(f);
 
     // get new label
     const M oldLabel = choice->label();
@@ -826,13 +824,14 @@ namespace gtsam {
     /// Do a depth-first visit on the tree rooted at node.
     void operator()(const typename DecisionTree<L, Y>::NodePtr& node) const {
       using Leaf = typename DecisionTree<L, Y>::Leaf;
-      if (auto leaf = std::dynamic_pointer_cast<const Leaf>(node))
-        return f(leaf->constant());
-
       using Choice = typename DecisionTree<L, Y>::Choice;
-      auto choice = std::dynamic_pointer_cast<const Choice>(node);
-      if (!choice)
-        throw std::invalid_argument("DecisionTree::Visit: Invalid NodePtr");
+
+      if (node->isLeaf()) {
+        auto leaf = std::static_pointer_cast<const Leaf>(node);
+        return f(leaf->constant());
+      }
+
+      auto choice = std::static_pointer_cast<const Choice>(node);
       for (auto&& branch : choice->branches()) (*this)(branch);  // recurse!
     }
   };
@@ -863,13 +862,14 @@ namespace gtsam {
     /// Do a depth-first visit on the tree rooted at node.
     void operator()(const typename DecisionTree<L, Y>::NodePtr& node) const {
       using Leaf = typename DecisionTree<L, Y>::Leaf;
-      if (auto leaf = std::dynamic_pointer_cast<const Leaf>(node))
-        return f(*leaf);
-
       using Choice = typename DecisionTree<L, Y>::Choice;
-      auto choice = std::dynamic_pointer_cast<const Choice>(node);
-      if (!choice)
-        throw std::invalid_argument("DecisionTree::VisitLeaf: Invalid NodePtr");
+
+      if (node->isLeaf()) {
+        auto leaf = std::static_pointer_cast<const Leaf>(node);
+        return f(*leaf);
+      }
+
+      auto choice = std::static_pointer_cast<const Choice>(node);
       for (auto&& branch : choice->branches()) (*this)(branch);  // recurse!
     }
   };
@@ -898,13 +898,16 @@ namespace gtsam {
     /// Do a depth-first visit on the tree rooted at node.
     void operator()(const typename DecisionTree<L, Y>::NodePtr& node) {
       using Leaf = typename DecisionTree<L, Y>::Leaf;
-      if (auto leaf = std::dynamic_pointer_cast<const Leaf>(node))
-        return f(assignment, leaf->constant());
-
       using Choice = typename DecisionTree<L, Y>::Choice;
-      auto choice = std::dynamic_pointer_cast<const Choice>(node);
-      if (!choice)
-        throw std::invalid_argument("DecisionTree::VisitWith: Invalid NodePtr");
+
+      if (node->isLeaf()) {
+        auto leaf = std::static_pointer_cast<const Leaf>(node);
+        return f(assignment, leaf->constant());
+      }
+
+
+
+      auto choice = std::static_pointer_cast<const Choice>(node);
       for (size_t i = 0; i < choice->nrChoices(); i++) {
         assignment[choice->label()] = i;  // Set assignment for label to i
 
diff --git a/gtsam/discrete/DecisionTreeFactor.h b/gtsam/discrete/DecisionTreeFactor.h
index 4da5a7c17..716c43b63 100644
--- a/gtsam/discrete/DecisionTreeFactor.h
+++ b/gtsam/discrete/DecisionTreeFactor.h
@@ -164,6 +164,12 @@ namespace gtsam {
     virtual DiscreteFactor::shared_ptr multiply(
         const DiscreteFactor::shared_ptr& f) const override;
 
+    /// multiply with a scalar
+    DiscreteFactor::shared_ptr operator*(double s) const override {
+      return std::make_shared<DecisionTreeFactor>(
+          apply([s](const double& a) { return Ring::mul(a, s); }));
+    }
+
     /// multiply two factors
     DecisionTreeFactor operator*(const DecisionTreeFactor& f) const override {
       return apply(f, Ring::mul);
@@ -201,6 +207,9 @@ namespace gtsam {
       return combine(keys, Ring::add);
     }
 
+    /// Find the maximum value in the factor.
+    double max() const override { return ADT::max(); };
+
     /// Create new factor by maximizing over all values with the same separator.
     DiscreteFactor::shared_ptr max(size_t nrFrontals) const override {
       return combine(nrFrontals, Ring::max);
diff --git a/gtsam/discrete/DiscreteBayesNet.cpp b/gtsam/discrete/DiscreteBayesNet.cpp
index 8c04cb91c..12c607223 100644
--- a/gtsam/discrete/DiscreteBayesNet.cpp
+++ b/gtsam/discrete/DiscreteBayesNet.cpp
@@ -89,7 +89,7 @@ DiscreteBayesNet DiscreteBayesNet::prune(
   DiscreteValues deadModesValues;
   // If we have a dead mode threshold and discrete variables left after pruning,
   // then we run dead mode removal.
-  if (marginalThreshold.has_value() && pruned.keys().size() > 0) {
+  if (marginalThreshold && pruned.keys().size() > 0) {
     DiscreteMarginals marginals(DiscreteFactorGraph{pruned});
     for (auto dkey : pruned.discreteKeys()) {
       const Vector probabilities = marginals.marginalProbabilities(dkey);
diff --git a/gtsam/discrete/DiscreteFactor.cpp b/gtsam/discrete/DiscreteFactor.cpp
index faae02af2..61b4c135c 100644
--- a/gtsam/discrete/DiscreteFactor.cpp
+++ b/gtsam/discrete/DiscreteFactor.cpp
@@ -73,10 +73,7 @@ AlgebraicDecisionTree<Key> DiscreteFactor::errorTree() const {
 
 /* ************************************************************************ */
 DiscreteFactor::shared_ptr DiscreteFactor::scale() const {
-  // Max over all the potentials by pretending all keys are frontal:
-  shared_ptr denominator = this->max(this->size());
-  // Normalize the product factor to prevent underflow.
-  return this->operator/(denominator);
+  return this->operator*(1.0 / max());
 }
 
 }  // namespace gtsam
diff --git a/gtsam/discrete/DiscreteFactor.h b/gtsam/discrete/DiscreteFactor.h
index fafb4dbf5..6fa074379 100644
--- a/gtsam/discrete/DiscreteFactor.h
+++ b/gtsam/discrete/DiscreteFactor.h
@@ -126,6 +126,9 @@ class GTSAM_EXPORT DiscreteFactor : public Factor {
   /// Compute error for each assignment and return as a tree
   virtual AlgebraicDecisionTree<Key> errorTree() const;
 
+  /// Multiply with a scalar
+  virtual DiscreteFactor::shared_ptr operator*(double s) const = 0;
+
   /// Multiply in a DecisionTreeFactor and return the result as
   /// DecisionTreeFactor
   virtual DecisionTreeFactor operator*(const DecisionTreeFactor&) const = 0;
@@ -152,6 +155,9 @@ class GTSAM_EXPORT DiscreteFactor : public Factor {
   /// Create new factor by summing all values with the same separator values
   virtual DiscreteFactor::shared_ptr sum(const Ordering& keys) const = 0;
 
+  /// Find the maximum value in the factor.
+  virtual double max() const = 0;
+
   /// Create new factor by maximizing over all values with the same separator.
   virtual DiscreteFactor::shared_ptr max(size_t nrFrontals) const = 0;
 
diff --git a/gtsam/discrete/DiscreteFactorGraph.cpp b/gtsam/discrete/DiscreteFactorGraph.cpp
index 6f1f2d592..aec239d83 100644
--- a/gtsam/discrete/DiscreteFactorGraph.cpp
+++ b/gtsam/discrete/DiscreteFactorGraph.cpp
@@ -65,15 +65,10 @@ namespace gtsam {
 
   /* ************************************************************************ */
   DiscreteFactor::shared_ptr DiscreteFactorGraph::product() const {
-    DiscreteFactor::shared_ptr result;
-    for (auto it = this->begin(); it != this->end(); ++it) {
-      if (*it) {
-        if (result) {
-          result = result->multiply(*it);
-        } else {
-          // Assign to the first non-null factor
-          result = *it;
-        }
+    DiscreteFactor::shared_ptr result = nullptr;
+    for (const auto& factor : *this) {
+      if (factor) {
+        result = result ? result->multiply(factor) : factor;
       }
     }
     return result;
@@ -120,15 +115,7 @@ namespace gtsam {
 
   /* ************************************************************************ */
   DiscreteFactor::shared_ptr DiscreteFactorGraph::scaledProduct() const {
-    // PRODUCT: multiply all factors
-    gttic(product);
-    DiscreteFactor::shared_ptr product = this->product();
-    gttoc(product);
-
-    // Normalize the product factor to prevent underflow.
-    product = product->scale();
-
-    return product;
+    return product()->scale();
   }
 
   /* ************************************************************************ */
@@ -216,7 +203,7 @@ namespace gtsam {
                     const Ordering& frontalKeys) {
     gttic(product);
     // `product` is scaled later to prevent underflow.
-    DiscreteFactor::shared_ptr product = factors.product();
+    DiscreteFactor::shared_ptr product = factors.scaledProduct();
     gttoc(product);
 
     // sum out frontals, this is the factor on the separator
@@ -224,16 +211,6 @@ namespace gtsam {
     DiscreteFactor::shared_ptr sum = product->sum(frontalKeys);
     gttoc(sum);
 
-    // Normalize/scale to prevent underflow.
-    // We divide both `product` and `sum` by `max(sum)`
-    // since it is faster to compute and when the conditional
-    // is formed by `product/sum`, the scaling term cancels out.
-    // gttic(scale);
-    // DiscreteFactor::shared_ptr denominator = sum->max(sum->size());
-    // product = product->operator/(denominator);
-    // sum = sum->operator/(denominator);
-    // gttoc(scale);
-
     // Ordering keys for the conditional so that frontalKeys are really in front
     Ordering orderedKeys;
     orderedKeys.insert(orderedKeys.end(), frontalKeys.begin(),
diff --git a/gtsam/discrete/TableDistribution.cpp b/gtsam/discrete/TableDistribution.cpp
index e8696c5b1..ce0d92bff 100644
--- a/gtsam/discrete/TableDistribution.cpp
+++ b/gtsam/discrete/TableDistribution.cpp
@@ -110,6 +110,11 @@ DiscreteFactor::shared_ptr TableDistribution::max(const Ordering& keys) const {
   return table_.max(keys);
 }
 
+/* ****************************************************************************/
+DiscreteFactor::shared_ptr TableDistribution::operator*(double s) const {
+  return table_ * s;
+}
+
 /* ****************************************************************************/
 DiscreteFactor::shared_ptr TableDistribution::operator/(
     const DiscreteFactor::shared_ptr& f) const {
diff --git a/gtsam/discrete/TableDistribution.h b/gtsam/discrete/TableDistribution.h
index 72786a515..8e28bed5f 100644
--- a/gtsam/discrete/TableDistribution.h
+++ b/gtsam/discrete/TableDistribution.h
@@ -116,12 +116,19 @@ class GTSAM_EXPORT TableDistribution : public DiscreteConditional {
   /// Create new factor by summing all values with the same separator values
   DiscreteFactor::shared_ptr sum(const Ordering& keys) const override;
 
+  /// Find the maximum value in the factor.
+  double max() const override { return table_.max(); }
+
   /// Create new factor by maximizing over all values with the same separator.
   DiscreteFactor::shared_ptr max(size_t nrFrontals) const override;
 
   /// Create new factor by maximizing over all values with the same separator.
   DiscreteFactor::shared_ptr max(const Ordering& keys) const override;
 
+
+  /// Multiply by scalar s
+  DiscreteFactor::shared_ptr operator*(double s) const override;
+
   /// divide by DiscreteFactor::shared_ptr f (safely)
   DiscreteFactor::shared_ptr operator/(
       const DiscreteFactor::shared_ptr& f) const override;
diff --git a/gtsam/discrete/TableFactor.cpp b/gtsam/discrete/TableFactor.cpp
index d1cedc9ef..25acae06e 100644
--- a/gtsam/discrete/TableFactor.cpp
+++ b/gtsam/discrete/TableFactor.cpp
@@ -389,6 +389,36 @@ void TableFactor::print(const string& s, const KeyFormatter& formatter) const {
   cout << "number of nnzs: " << sparse_table_.nonZeros() << endl;
 }
 
+/* ************************************************************************ */
+DiscreteFactor::shared_ptr TableFactor::sum(size_t nrFrontals) const {
+return combine(nrFrontals, Ring::add);
+}
+
+/* ************************************************************************ */
+DiscreteFactor::shared_ptr TableFactor::sum(const Ordering& keys) const {
+return combine(keys, Ring::add);
+}
+
+/* ************************************************************************ */
+double TableFactor::max() const {
+  double max_value = std::numeric_limits<double>::lowest();
+  for (Eigen::SparseVector<double>::InnerIterator it(sparse_table_); it; ++it) {
+    max_value = std::max(max_value, it.value());
+  }
+  return max_value;
+}
+
+/* ************************************************************************ */
+DiscreteFactor::shared_ptr TableFactor::max(size_t nrFrontals) const {
+  return combine(nrFrontals, Ring::max);
+}
+
+/* ************************************************************************ */
+DiscreteFactor::shared_ptr TableFactor::max(const Ordering& keys) const {
+  return combine(keys, Ring::max);
+}
+
+
 /* ************************************************************************ */
 TableFactor TableFactor::apply(Unary op) const {
   // Initialize new factor.
diff --git a/gtsam/discrete/TableFactor.h b/gtsam/discrete/TableFactor.h
index 1cb9eda8b..ce58d14bc 100644
--- a/gtsam/discrete/TableFactor.h
+++ b/gtsam/discrete/TableFactor.h
@@ -171,6 +171,12 @@ class GTSAM_EXPORT TableFactor : public DiscreteFactor {
   /// Calculate error for DiscreteValues `x`, is -log(probability).
   double error(const DiscreteValues& values) const override;
 
+  /// multiply with a scalar
+  DiscreteFactor::shared_ptr operator*(double s) const override {
+    return std::make_shared<TableFactor>(
+        apply([s](const double& a) { return Ring::mul(a, s); }));
+  }
+
   /// multiply two TableFactors
   TableFactor operator*(const TableFactor& f) const {
     return apply(f, Ring::mul);
@@ -215,24 +221,19 @@ class GTSAM_EXPORT TableFactor : public DiscreteFactor {
                      DiscreteKeys parent_keys) const;
 
   /// Create new factor by summing all values with the same separator values
-  DiscreteFactor::shared_ptr sum(size_t nrFrontals) const override {
-    return combine(nrFrontals, Ring::add);
-  }
+  DiscreteFactor::shared_ptr sum(size_t nrFrontals) const override;
 
   /// Create new factor by summing all values with the same separator values
-  DiscreteFactor::shared_ptr sum(const Ordering& keys) const override {
-    return combine(keys, Ring::add);
-  }
+  DiscreteFactor::shared_ptr sum(const Ordering& keys) const override;
+
+  /// Find the maximum value in the factor.
+  double max() const override;
 
   /// Create new factor by maximizing over all values with the same separator.
-  DiscreteFactor::shared_ptr max(size_t nrFrontals) const override {
-    return combine(nrFrontals, Ring::max);
-  }
+  DiscreteFactor::shared_ptr max(size_t nrFrontals) const override;
 
   /// Create new factor by maximizing over all values with the same separator.
-  DiscreteFactor::shared_ptr max(const Ordering& keys) const override {
-    return combine(keys, Ring::max);
-  }
+  DiscreteFactor::shared_ptr max(const Ordering& keys) const override;
 
   /// @}
   /// @name Advanced Interface
diff --git a/gtsam/hybrid/HybridBayesNet.cpp b/gtsam/hybrid/HybridBayesNet.cpp
index 67d2104d2..5f36f81f1 100644
--- a/gtsam/hybrid/HybridBayesNet.cpp
+++ b/gtsam/hybrid/HybridBayesNet.cpp
@@ -65,6 +65,7 @@ HybridBayesNet HybridBayesNet::prune(
   }
 
   HybridBayesNet result;
+  result.reserve(size());
 
   // Go through all the Gaussian conditionals, restrict them according to
   // fixed values, and then prune further.
@@ -84,9 +85,9 @@ HybridBayesNet HybridBayesNet::prune(
       }
       // Type-erase and add to the pruned Bayes Net fragment.
       result.push_back(prunedHybridGaussianConditional);
-    } else if (auto gc = conditional->asGaussian()) {
-      // Add the non-HybridGaussianConditional conditional
-      result.push_back(gc);
+    } else if (conditional->isContinuous()) {
+      // Add the non-Hybrid GaussianConditional conditional
+      result.push_back(conditional);
     } else
       throw std::runtime_error(
           "HybrdiBayesNet::prune: Unknown HybridConditional type.");
diff --git a/gtsam/hybrid/HybridFactor.cpp b/gtsam/hybrid/HybridFactor.cpp
index 3338951bf..627da4fe6 100644
--- a/gtsam/hybrid/HybridFactor.cpp
+++ b/gtsam/hybrid/HybridFactor.cpp
@@ -23,6 +23,7 @@ namespace gtsam {
 KeyVector CollectKeys(const KeyVector &continuousKeys,
                       const DiscreteKeys &discreteKeys) {
   KeyVector allKeys;
+  allKeys.reserve(continuousKeys.size() + discreteKeys.size());
   std::copy(continuousKeys.begin(), continuousKeys.end(),
             std::back_inserter(allKeys));
   std::transform(discreteKeys.begin(), discreteKeys.end(),
@@ -34,6 +35,7 @@ KeyVector CollectKeys(const KeyVector &continuousKeys,
 /* ************************************************************************ */
 KeyVector CollectKeys(const KeyVector &keys1, const KeyVector &keys2) {
   KeyVector allKeys;
+  allKeys.reserve(keys1.size() + keys2.size());
   std::copy(keys1.begin(), keys1.end(), std::back_inserter(allKeys));
   std::copy(keys2.begin(), keys2.end(), std::back_inserter(allKeys));
   return allKeys;
diff --git a/gtsam/hybrid/HybridGaussianConditional.cpp b/gtsam/hybrid/HybridGaussianConditional.cpp
index 964af7ffb..0546ff16b 100644
--- a/gtsam/hybrid/HybridGaussianConditional.cpp
+++ b/gtsam/hybrid/HybridGaussianConditional.cpp
@@ -191,11 +191,19 @@ size_t HybridGaussianConditional::nrComponents() const {
 /* *******************************************************************************/
 GaussianConditional::shared_ptr HybridGaussianConditional::choose(
     const DiscreteValues &discreteValues) const {
-  auto &[factor, _] = factors()(discreteValues);
-  if (!factor) return nullptr;
+  try {
+    auto &[factor, _] = factors()(discreteValues);
+    if (!factor) return nullptr;
 
-  auto conditional = checkConditional(factor);
-  return conditional;
+    auto conditional = checkConditional(factor);
+    return conditional;
+  } catch (const std::out_of_range &e) {
+    GTSAM_PRINT(*this);
+    GTSAM_PRINT(discreteValues);
+    throw std::runtime_error(
+        "HybridGaussianConditional::choose: discreteValues does not contain "
+        "all discrete parents.");
+  }
 }
 
 /* *******************************************************************************/
diff --git a/gtsam/hybrid/HybridGaussianFactorGraph.cpp b/gtsam/hybrid/HybridGaussianFactorGraph.cpp
index cfe5c4b59..b0bd17131 100644
--- a/gtsam/hybrid/HybridGaussianFactorGraph.cpp
+++ b/gtsam/hybrid/HybridGaussianFactorGraph.cpp
@@ -50,7 +50,7 @@
 #include <utility>
 #include <vector>
 
-#define GTSAM_HYBRID_WITH_TABLEFACTOR 0
+#define GTSAM_HYBRID_WITH_TABLEFACTOR 1
 
 namespace gtsam {
 
diff --git a/gtsam/hybrid/HybridSmoother.cpp b/gtsam/hybrid/HybridSmoother.cpp
index dfbbbcfe2..a67777b52 100644
--- a/gtsam/hybrid/HybridSmoother.cpp
+++ b/gtsam/hybrid/HybridSmoother.cpp
@@ -21,55 +21,70 @@
 #include <algorithm>
 #include <unordered_set>
 
+// #define DEBUG_SMOOTHER
 namespace gtsam {
 
 /* ************************************************************************* */
 Ordering HybridSmoother::getOrdering(const HybridGaussianFactorGraph &factors,
-                                     const KeySet &newFactorKeys) {
+                                     const KeySet &lastKeysToEliminate) {
   // Get all the discrete keys from the factors
   KeySet allDiscrete = factors.discreteKeySet();
 
   // Create KeyVector with continuous keys followed by discrete keys.
-  KeyVector newKeysDiscreteLast;
+  KeyVector lastKeys;
 
   // Insert continuous keys first.
-  for (auto &k : newFactorKeys) {
+  for (auto &k : lastKeysToEliminate) {
     if (!allDiscrete.exists(k)) {
-      newKeysDiscreteLast.push_back(k);
+      lastKeys.push_back(k);
     }
   }
 
   // Insert discrete keys at the end
   std::copy(allDiscrete.begin(), allDiscrete.end(),
-            std::back_inserter(newKeysDiscreteLast));
-
-  const VariableIndex index(factors);
+            std::back_inserter(lastKeys));
 
   // Get an ordering where the new keys are eliminated last
   Ordering ordering = Ordering::ColamdConstrainedLast(
-      index, KeyVector(newKeysDiscreteLast.begin(), newKeysDiscreteLast.end()),
-      true);
+      factors, KeyVector(lastKeys.begin(), lastKeys.end()), true);
+
   return ordering;
 }
 
 /* ************************************************************************* */
-void HybridSmoother::update(const HybridGaussianFactorGraph &graph,
+void HybridSmoother::update(const HybridGaussianFactorGraph &newFactors,
                             std::optional<size_t> maxNrLeaves,
                             const std::optional<Ordering> given_ordering) {
+  const KeySet originalNewFactorKeys = newFactors.keys();
+#ifdef DEBUG_SMOOTHER
+  std::cout << "hybridBayesNet_ size before: " << hybridBayesNet_.size()
+            << std::endl;
+  std::cout << "newFactors size: " << newFactors.size() << std::endl;
+#endif
   HybridGaussianFactorGraph updatedGraph;
   // Add the necessary conditionals from the previous timestep(s).
   std::tie(updatedGraph, hybridBayesNet_) =
-      addConditionals(graph, hybridBayesNet_);
+      addConditionals(newFactors, hybridBayesNet_);
+#ifdef DEBUG_SMOOTHER
+  // print size of newFactors, updatedGraph, hybridBayesNet_
+  std::cout << "updatedGraph size: " << updatedGraph.size() << std::endl;
+  std::cout << "hybridBayesNet_ size after: " << hybridBayesNet_.size()
+            << std::endl;
+  std::cout << "total size: " << updatedGraph.size() + hybridBayesNet_.size()
+            << std::endl;
+#endif
 
   Ordering ordering;
   // If no ordering provided, then we compute one
   if (!given_ordering.has_value()) {
     // Get the keys from the new factors
-    const KeySet newFactorKeys = graph.keys();
+    KeySet continuousKeysToInclude;  // Scheme 1: empty, 15sec/2000, 64sec/3000 (69s without TF)
+    // continuousKeysToInclude = newFactors.keys();  // Scheme 2: all, 8sec/2000, 160sec/3000
+    // continuousKeysToInclude = updatedGraph.keys();  // Scheme 3: all, stopped after 80sec/2000
 
     // Since updatedGraph now has all the connected conditionals,
     // we can get the correct ordering.
-    ordering = this->getOrdering(updatedGraph, newFactorKeys);
+    ordering = this->getOrdering(updatedGraph, continuousKeysToInclude);
   } else {
     ordering = *given_ordering;
   }
@@ -83,6 +98,22 @@ void HybridSmoother::update(const HybridGaussianFactorGraph &graph,
   gttoc_(HybridSmootherEliminate);
 #endif
 
+#ifdef DEBUG_SMOOTHER_DETAIL
+  for (auto conditional : bayesNetFragment) {
+    auto e = std::dynamic_pointer_cast<HybridConditional::BaseConditional>(
+        conditional);
+    GTSAM_PRINT(*e);
+  }
+#endif
+
+#ifdef DEBUG_SMOOTHER
+  // Print discrete keys in the bayesNetFragment:
+  std::cout << "Discrete keys in bayesNetFragment: ";
+  for (auto &key : HybridFactorGraph(bayesNetFragment).discreteKeySet()) {
+    std::cout << DefaultKeyFormatter(key) << " ";
+  }
+#endif
+
   /// Prune
   if (maxNrLeaves) {
 #if GTSAM_HYBRID_TIMING
@@ -90,24 +121,47 @@ void HybridSmoother::update(const HybridGaussianFactorGraph &graph,
 #endif
     // `pruneBayesNet` sets the leaves with 0 in discreteFactor to nullptr in
     // all the conditionals with the same keys in bayesNetFragment.
-    bayesNetFragment = bayesNetFragment.prune(*maxNrLeaves, marginalThreshold_);
+    DiscreteValues newlyFixedValues;
+    bayesNetFragment = bayesNetFragment.prune(*maxNrLeaves, marginalThreshold_,
+                                              &newlyFixedValues);
+    fixedValues_.insert(newlyFixedValues);
 #if GTSAM_HYBRID_TIMING
     gttoc_(HybridSmootherPrune);
 #endif
   }
 
+#ifdef DEBUG_SMOOTHER
+  // Print discrete keys in the bayesNetFragment:
+  std::cout << "\nAfter pruning: ";
+  for (auto &key : HybridFactorGraph(bayesNetFragment).discreteKeySet()) {
+    std::cout << DefaultKeyFormatter(key) << " ";
+  }
+  std::cout << std::endl << std::endl;
+#endif
+
+#ifdef DEBUG_SMOOTHER_DETAIL
+  for (auto conditional : bayesNetFragment) {
+    auto c = std::dynamic_pointer_cast<HybridConditional::BaseConditional>(
+        conditional);
+    GTSAM_PRINT(*c);
+  }
+#endif
+
   // Add the partial bayes net to the posterior bayes net.
   hybridBayesNet_.add(bayesNetFragment);
 }
 
 /* ************************************************************************* */
 std::pair<HybridGaussianFactorGraph, HybridBayesNet>
-HybridSmoother::addConditionals(const HybridGaussianFactorGraph &originalGraph,
+HybridSmoother::addConditionals(const HybridGaussianFactorGraph &newFactors,
                                 const HybridBayesNet &hybridBayesNet) const {
-  HybridGaussianFactorGraph graph(originalGraph);
+  HybridGaussianFactorGraph graph(newFactors);
   HybridBayesNet updatedHybridBayesNet(hybridBayesNet);
 
-  KeySet factorKeys = graph.keys();
+  KeySet involvedKeys = newFactors.keys();
+  auto involved = [&involvedKeys](const Key &key) {
+    return involvedKeys.find(key) != involvedKeys.end();
+  };
 
   // If hybridBayesNet is not empty,
   // it means we have conditionals to add to the factor graph.
@@ -129,25 +183,26 @@ HybridSmoother::addConditionals(const HybridGaussianFactorGraph &originalGraph,
       auto conditional = hybridBayesNet.at(i);
 
       for (auto &key : conditional->frontals()) {
-        if (std::find(factorKeys.begin(), factorKeys.end(), key) !=
-            factorKeys.end()) {
-          // Add the conditional parents to factorKeys
+        if (involved(key)) {
+          // Add the conditional parents to involvedKeys
           // so we add those conditionals too.
           for (auto &&parentKey : conditional->parents()) {
-            factorKeys.insert(parentKey);
+            involvedKeys.insert(parentKey);
           }
           // Break so we don't add parents twice.
           break;
         }
       }
     }
+#ifdef DEBUG_SMOOTHER
+    PrintKeySet(involvedKeys);
+#endif
 
     for (size_t i = 0; i < hybridBayesNet.size(); i++) {
       auto conditional = hybridBayesNet.at(i);
 
       for (auto &key : conditional->frontals()) {
-        if (std::find(factorKeys.begin(), factorKeys.end(), key) !=
-            factorKeys.end()) {
+        if (involved(key)) {
           newConditionals.push_back(conditional);
 
           // Remove the conditional from the updated Bayes net
@@ -177,4 +232,21 @@ const HybridBayesNet &HybridSmoother::hybridBayesNet() const {
   return hybridBayesNet_;
 }
 
+/* ************************************************************************* */
+HybridValues HybridSmoother::optimize() const {
+  // Solve for the MPE
+  DiscreteValues mpe = hybridBayesNet_.mpe();
+
+  // Add fixed values to the MPE.
+  mpe.insert(fixedValues_);
+
+  // Given the MPE, compute the optimal continuous values.
+  GaussianBayesNet gbn = hybridBayesNet_.choose(mpe);
+  const VectorValues continuous = gbn.optimize();
+  if (std::find(gbn.begin(), gbn.end(), nullptr) != gbn.end()) {
+    throw std::runtime_error("At least one nullptr factor in hybridBayesNet_");
+  }
+  return HybridValues(continuous, mpe);
+}
+
 }  // namespace gtsam
diff --git a/gtsam/hybrid/HybridSmoother.h b/gtsam/hybrid/HybridSmoother.h
index 2f7bfcebb..12da3b0af 100644
--- a/gtsam/hybrid/HybridSmoother.h
+++ b/gtsam/hybrid/HybridSmoother.h
@@ -106,6 +106,9 @@ class GTSAM_EXPORT HybridSmoother {
 
   /// Return the Bayes Net posterior.
   const HybridBayesNet& hybridBayesNet() const;
+
+  /// Optimize the hybrid Bayes Net, taking into accound fixed values.
+  HybridValues optimize() const;
 };
 
 }  // namespace gtsam
diff --git a/gtsam/hybrid/tests/testHybridConditional.cpp b/gtsam/hybrid/tests/testHybridConditional.cpp
index 365dde3bc..216acdb4e 100644
--- a/gtsam/hybrid/tests/testHybridConditional.cpp
+++ b/gtsam/hybrid/tests/testHybridConditional.cpp
@@ -28,6 +28,28 @@ using symbol_shorthand::M;
 using symbol_shorthand::X;
 using symbol_shorthand::Z;
 
+/* ****************************************************************************/
+// Test the HybridConditional constructor.
+TEST(HybridConditional, Constructor) {
+  // Create a HybridGaussianConditional.
+  const KeyVector continuousKeys{X(0), X(1)};
+  const DiscreteKeys discreteKeys{{M(0), 2}};
+  const size_t nFrontals = 1;
+  const HybridConditional hc(continuousKeys, discreteKeys, nFrontals);
+
+  // Check Frontals:
+  EXPECT_LONGS_EQUAL(1, hc.nrFrontals());
+  const auto frontals = hc.frontals();
+  EXPECT_LONGS_EQUAL(1, frontals.size());
+  EXPECT_LONGS_EQUAL(X(0), *frontals.begin());
+
+  // Check parents:
+  const auto parents = hc.parents();
+  EXPECT_LONGS_EQUAL(2, parents.size());
+  EXPECT_LONGS_EQUAL(X(1), *parents.begin());
+  EXPECT_LONGS_EQUAL(M(0), *(parents.begin() + 1));
+}
+
 /* ****************************************************************************/
 // Check invariants for all conditionals in a tiny Bayes net.
 TEST(HybridConditional, Invariants) {
@@ -43,6 +65,12 @@ TEST(HybridConditional, Invariants) {
   auto hc0 = bn.at(0);
   CHECK(hc0->isHybrid());
 
+  // Check parents:
+  const auto parents = hc0->parents();
+  EXPECT_LONGS_EQUAL(2, parents.size());
+  EXPECT_LONGS_EQUAL(X(0), *parents.begin());
+  EXPECT_LONGS_EQUAL(M(0), *(parents.begin() + 1));
+
   // Check invariants as a HybridGaussianConditional.
   const auto conditional = hc0->asHybrid();
   EXPECT(HybridGaussianConditional::CheckInvariants(*conditional, values));
diff --git a/gtsam/linear/HessianFactor.cpp b/gtsam/linear/HessianFactor.cpp
index 0a75cc336..739582716 100644
--- a/gtsam/linear/HessianFactor.cpp
+++ b/gtsam/linear/HessianFactor.cpp
@@ -467,7 +467,7 @@ std::shared_ptr<GaussianConditional> HessianFactor::eliminateCholesky(const Orde
     info_.choleskyPartial(nFrontals);
 
     // TODO(frank): pre-allocate GaussianConditional and write into it
-    const VerticalBlockMatrix Ab = info_.split(nFrontals);
+    VerticalBlockMatrix Ab = info_.split(nFrontals);
     conditional = std::make_shared<GaussianConditional>(keys_, nFrontals, std::move(Ab));
 
     // Erase the eliminated keys in this factor
diff --git a/gtsam_unstable/discrete/Constraint.h b/gtsam_unstable/discrete/Constraint.h
index 328fabbea..637cf404e 100644
--- a/gtsam_unstable/discrete/Constraint.h
+++ b/gtsam_unstable/discrete/Constraint.h
@@ -87,6 +87,16 @@ class GTSAM_UNSTABLE_EXPORT Constraint : public DiscreteFactor {
         this->operator*(df->toDecisionTreeFactor()));
   }
 
+  /// Multiply by a scalar
+  virtual DiscreteFactor::shared_ptr operator*(double s) const override {
+    return this->toDecisionTreeFactor() * s;
+  }
+
+  /// Multiply by a DecisionTreeFactor and return a DecisionTreeFactor
+  DecisionTreeFactor operator*(const DecisionTreeFactor& dtf) const override {
+    return this->toDecisionTreeFactor() * dtf;
+  }
+
   /// divide by DiscreteFactor::shared_ptr f (safely)
   DiscreteFactor::shared_ptr operator/(
       const DiscreteFactor::shared_ptr& df) const override {
@@ -104,6 +114,9 @@ class GTSAM_UNSTABLE_EXPORT Constraint : public DiscreteFactor {
     return toDecisionTreeFactor().sum(keys);
   }
 
+  /// Find the max value
+  double max() const override { return toDecisionTreeFactor().max(); }
+
   DiscreteFactor::shared_ptr max(size_t nrFrontals) const override {
     return toDecisionTreeFactor().max(nrFrontals);
   }