diff --git a/gtsam/discrete/DiscreteSearch.cpp b/gtsam/discrete/DiscreteSearch.cpp
index 439331fa1..4270dfbf7 100644
--- a/gtsam/discrete/DiscreteSearch.cpp
+++ b/gtsam/discrete/DiscreteSearch.cpp
@@ -150,21 +150,58 @@ class Solutions {
   }
 };
 
-DiscreteSearch::DiscreteSearch(const DiscreteFactorGraph& factorGraph,
-                               const Ordering& ordering,
-                               bool buildJunctionTree) {
-  const DiscreteEliminationTree etree(factorGraph, ordering);
-  const DiscreteJunctionTree junctionTree(etree);
+DiscreteSearch::DiscreteSearch(const DiscreteEliminationTree& etree) {
+  using NodePtr = std::shared_ptr<DiscreteEliminationTree::Node>;
+  auto visitor = [this](const NodePtr& node, int data) {
+    const auto& factors = node->factors;
+    const auto factor = factors.size() == 1
+                            ? factors.back()
+                            : DiscreteFactorGraph(factors).product();
+    const size_t cardinality = factor->cardinality(node->key);
+    std::vector<std::pair<Key, size_t>> pairs{{node->key, cardinality}};
+    slots_.emplace_back(factor, DiscreteValues::CartesianProduct(pairs), 0.0);
+    return data + 1;
+  };
 
-  // GTSAM_PRINT(asia::etree);
-  // GTSAM_PRINT(asia::junctionTree);
-  slots_.reserve(factorGraph.size());
-  for (auto& factor : factorGraph) {
-    slots_.emplace_back(factor, std::vector<DiscreteValues>{}, 0.0);
-  }
+  const int data = 0;  // unused
+  treeTraversal::DepthFirstForest(etree, data, visitor);
+  std::reverse(slots_.begin(), slots_.end());  // reverse slots
   lowerBound_ = computeHeuristic();
 }
 
+DiscreteSearch::DiscreteSearch(const DiscreteJunctionTree& junctionTree) {
+  using NodePtr = std::shared_ptr<DiscreteJunctionTree::Cluster>;
+  auto visitor = [this](const NodePtr& cluster, int data) {
+    const auto& factors = cluster->factors;
+    const auto factor = factors.size() == 1
+                            ? factors.back()
+                            : DiscreteFactorGraph(factors).product();
+    std::vector<std::pair<Key, size_t>> pairs;
+    for (Key key : cluster->orderedFrontalKeys) {
+      pairs.emplace_back(key, factor->cardinality(key));
+    }
+    slots_.emplace_back(factor, DiscreteValues::CartesianProduct(pairs), 0.0);
+    return data + 1;
+  };
+
+  const int data = 0;  // unused
+  treeTraversal::DepthFirstForest(junctionTree, data, visitor);
+  std::reverse(slots_.begin(), slots_.end());  // reverse slots
+  lowerBound_ = computeHeuristic();
+}
+
+DiscreteSearch DiscreteSearch::FromFactorGraph(
+    const DiscreteFactorGraph& factorGraph, const Ordering& ordering,
+    bool buildJunctionTree) {
+  const DiscreteEliminationTree etree(factorGraph, ordering);
+  if (buildJunctionTree) {
+    const DiscreteJunctionTree junctionTree(etree);
+    return DiscreteSearch(junctionTree);
+  } else {
+    return DiscreteSearch(etree);
+  }
+}
+
 DiscreteSearch::DiscreteSearch(const DiscreteBayesNet& bayesNet) {
   slots_.reserve(bayesNet.size());
   for (auto& conditional : bayesNet) {
@@ -188,6 +225,14 @@ DiscreteSearch::DiscreteSearch(const DiscreteBayesTree& bayesTree) {
   lowerBound_ = computeHeuristic();
 }
 
+void DiscreteSearch::print(const std::string& name,
+                           const KeyFormatter& formatter) const {
+  std::cout << name << " with " << slots_.size() << " slots:\n";
+  for (size_t i = 0; i < slots_.size(); ++i) {
+    std::cout << i << ": " << slots_[i] << std::endl;
+  }
+}
+
 struct SearchNodeQueue
     : public std::priority_queue<SearchNode, std::vector<SearchNode>,
                                  SearchNode::Compare> {
@@ -215,8 +260,6 @@ struct SearchNodeQueue
   }
 };
 
-#define DISCRETE_SEARCH_DEBUG
-
 std::vector<Solution> DiscreteSearch::run(size_t K) const {
   Solutions solutions(K);
   SearchNodeQueue expansions;
@@ -252,9 +295,9 @@ std::vector<Solution> DiscreteSearch::run(size_t K) const {
 // a lower-bound on the cost-to-go for each slot, *not* including this factor.
 // For the first slot, this is 0.0, as this is the last slot to be filled, so
 // the cost after that is zero. For the second slot, it is h0 =
-// -log(max(factor[0])), because after we assign slot[1] we still need to assign
-// slot[0], which will cost *at least* h0.
-// We return the estimated lower bound of the cost for *all* slots.
+// -log(max(factor[0])), because after we assign slot[1] we still need to
+// assign slot[0], which will cost *at least* h0. We return the estimated
+// lower bound of the cost for *all* slots.
 double DiscreteSearch::computeHeuristic() {
   double error = 0.0;
   for (size_t i = 0; i < slots_.size(); ++i) {
diff --git a/gtsam/discrete/DiscreteSearch.h b/gtsam/discrete/DiscreteSearch.h
index 3d5ee1d50..44e605e34 100644
--- a/gtsam/discrete/DiscreteSearch.h
+++ b/gtsam/discrete/DiscreteSearch.h
@@ -10,7 +10,11 @@
  * -------------------------------------------------------------------------- */
 
 /*
- * DiscreteSearch.cpp
+ * @file DiscreteSearch.h
+ * @brief Defines the DiscreteSearch class for discrete search algorithms.
+ *
+ * @details This file contains the definition of the DiscreteSearch class, which
+ * is used in discrete search algorithms to find the K best solutions.
  *
  * @date January, 2025
  * @author Frank Dellaert
@@ -43,6 +47,13 @@ class GTSAM_EXPORT DiscreteSearch {
     /// A lower bound on the cost-to-go for each slot, e.g.,
     /// [-log(max_B P(B|A)), -log(max_A P(A))]
     double heuristic;
+
+    friend std::ostream& operator<<(std::ostream& os, const Slot& slot) {
+      os << "Slot with " << slot.assignments.size()
+         << " assignments, heuristic=" << slot.heuristic;
+      os << ", factor:\n" << slot.factor->markdown() << std::endl;
+      return os;
+    }
   };
 
   /// A solution is then a set of assignments, covering all the slots.
@@ -59,6 +70,9 @@ class GTSAM_EXPORT DiscreteSearch {
   };
 
  public:
+  /// @name Standard Constructors
+  /// @{
+
   /**
    * Construct from a DiscreteFactorGraph.
    *
@@ -68,12 +82,26 @@ class GTSAM_EXPORT DiscreteSearch {
    * fine-grained (more slots).
    *
    * @param factorGraph The factor graph to search over.
-   * @param ordering The ordering of the variables to search over.
-   * @param buildJunctionTree Whether to build a junction tree for the factor
-   * graph.
+   * @param ordering The ordering used to create etree (and maybe jtree).
+   * @param buildJunctionTree Whether to build a junction tree or not.
    */
-  DiscreteSearch(const DiscreteFactorGraph& factorGraph,
-                 const Ordering& ordering, bool buildJunctionTree = false);
+  static DiscreteSearch FromFactorGraph(const DiscreteFactorGraph& factorGraph,
+                                        const Ordering& ordering,
+                                        bool buildJunctionTree = false);
+
+  /**
+   * @brief Constructor from a DiscreteEliminationTree.
+   *
+   * @param etree The DiscreteEliminationTree to initialize from.
+   */
+  DiscreteSearch(const DiscreteEliminationTree& etree);
+
+  /**
+   * @brief Constructor from a DiscreteJunctionTree.
+   *
+   * @param junctionTree The DiscreteJunctionTree to initialize from.
+   */
+  DiscreteSearch(const DiscreteJunctionTree& junctionTree);
 
   /**
    * Construct from a DiscreteBayesNet.
@@ -85,6 +113,18 @@ class GTSAM_EXPORT DiscreteSearch {
    */
   DiscreteSearch(const DiscreteBayesTree& bayesTree);
 
+  /// @}
+  /// @name Testable
+  /// @{
+
+  /** Print the tree to cout */
+  void print(const std::string& name = "DiscreteSearch: ",
+             const KeyFormatter& formatter = DefaultKeyFormatter) const;
+
+  /// @}
+  /// @name Standard API
+  /// @{
+
   /**
    * @brief Search for the K best solutions.
    *
@@ -97,6 +137,8 @@ class GTSAM_EXPORT DiscreteSearch {
    */
   std::vector<Solution> run(size_t K = 1) const;
 
+  /// @}
+
  private:
   /// Compute the cumulative lower-bound cost-to-go after each slot is filled.
   /// @return the estimated lower bound of the cost for *all* slots.