diff --git a/gtsam/discrete/DiscreteFactorGraph.cpp b/gtsam/discrete/DiscreteFactorGraph.cpp
index e05cf9e33..eb3221819 100644
--- a/gtsam/discrete/DiscreteFactorGraph.cpp
+++ b/gtsam/discrete/DiscreteFactorGraph.cpp
@@ -64,7 +64,7 @@ namespace gtsam {
   }
 
   /* ************************************************************************ */
-  DecisionTreeFactor DiscreteFactorGraph::product() const {
+  DiscreteFactor::shared_ptr DiscreteFactorGraph::product() const {
     DiscreteFactor::shared_ptr result;
     for (auto it = this->begin(); it != this->end(); ++it) {
       if (*it) {
@@ -76,7 +76,7 @@ namespace gtsam {
         }
       }
     }
-    return result->toDecisionTreeFactor();
+    return result;
   }
 
   /* ************************************************************************ */
@@ -122,20 +122,20 @@ namespace gtsam {
    * @brief Multiply all the `factors`.
    *
    * @param factors The factors to multiply as a DiscreteFactorGraph.
-   * @return DecisionTreeFactor
+   * @return DiscreteFactor::shared_ptr
    */
-  static DecisionTreeFactor DiscreteProduct(
+  static DiscreteFactor::shared_ptr DiscreteProduct(
       const DiscreteFactorGraph& factors) {
     // PRODUCT: multiply all factors
     gttic(product);
-    DecisionTreeFactor product = factors.product();
+    DiscreteFactor::shared_ptr product = factors.product();
     gttoc(product);
 
     // Max over all the potentials by pretending all keys are frontal:
-    auto denominator = product.max(product.size());
+    auto denominator = product->max(product->size());
 
     // Normalize the product factor to prevent underflow.
-    product = product / denominator;
+    product = product->operator/(denominator);
 
     return product;
   }
@@ -145,26 +145,25 @@ namespace gtsam {
   std::pair<DiscreteConditional::shared_ptr, DiscreteFactor::shared_ptr>  //
   EliminateForMPE(const DiscreteFactorGraph& factors,
                   const Ordering& frontalKeys) {
-    DecisionTreeFactor product = DiscreteProduct(factors);
+    DiscreteFactor::shared_ptr product = DiscreteProduct(factors);
 
     // max out frontals, this is the factor on the separator
     gttic(max);
-    DecisionTreeFactor::shared_ptr max =
-        std::dynamic_pointer_cast<DecisionTreeFactor>(product.max(frontalKeys));
+    DiscreteFactor::shared_ptr max = product->max(frontalKeys);
     gttoc(max);
 
     // Ordering keys for the conditional so that frontalKeys are really in front
     DiscreteKeys orderedKeys;
     for (auto&& key : frontalKeys)
-      orderedKeys.emplace_back(key, product.cardinality(key));
+      orderedKeys.emplace_back(key, product->cardinality(key));
     for (auto&& key : max->keys())
-      orderedKeys.emplace_back(key, product.cardinality(key));
+      orderedKeys.emplace_back(key, product->cardinality(key));
 
     // Make lookup with product
     gttic(lookup);
     size_t nrFrontals = frontalKeys.size();
-    auto lookup =
-        std::make_shared<DiscreteLookupTable>(nrFrontals, orderedKeys, product);
+    auto lookup = std::make_shared<DiscreteLookupTable>(
+        nrFrontals, orderedKeys, product->toDecisionTreeFactor());
     gttoc(lookup);
 
     return {std::dynamic_pointer_cast<DiscreteConditional>(lookup), max};
@@ -224,12 +223,11 @@ namespace gtsam {
   std::pair<DiscreteConditional::shared_ptr, DiscreteFactor::shared_ptr>  //
   EliminateDiscrete(const DiscreteFactorGraph& factors,
                     const Ordering& frontalKeys) {
-    DecisionTreeFactor product = DiscreteProduct(factors);
+    DiscreteFactor::shared_ptr product = DiscreteProduct(factors);
 
     // sum out frontals, this is the factor on the separator
     gttic(sum);
-    DecisionTreeFactor::shared_ptr sum = std::dynamic_pointer_cast<DecisionTreeFactor>(
-        product.sum(frontalKeys));
+    DiscreteFactor::shared_ptr sum = product->sum(frontalKeys);
     gttoc(sum);
 
     // Ordering keys for the conditional so that frontalKeys are really in front
@@ -241,8 +239,9 @@ namespace gtsam {
 
     // now divide product/sum to get conditional
     gttic(divide);
-    auto conditional =
-        std::make_shared<DiscreteConditional>(product, *sum, orderedKeys);
+    auto conditional = std::make_shared<DiscreteConditional>(
+        product->toDecisionTreeFactor(), sum->toDecisionTreeFactor(),
+        orderedKeys);
     gttoc(divide);
 
     return {conditional, sum};
diff --git a/gtsam/discrete/DiscreteFactorGraph.h b/gtsam/discrete/DiscreteFactorGraph.h
index b311cb78b..3d9e86cd1 100644
--- a/gtsam/discrete/DiscreteFactorGraph.h
+++ b/gtsam/discrete/DiscreteFactorGraph.h
@@ -148,7 +148,7 @@ class GTSAM_EXPORT DiscreteFactorGraph
   DiscreteKeys discreteKeys() const;
 
   /** return product of all factors as a single factor */
-  DecisionTreeFactor product() const;
+  DiscreteFactor::shared_ptr product() const;
 
   /** 
    * Evaluates the factor graph given values, returns the joint probability of