diff --git a/gtsam/discrete/DecisionTreeFactor.cpp b/gtsam/discrete/DecisionTreeFactor.cpp
index 04e29024c..ff18268b1 100644
--- a/gtsam/discrete/DecisionTreeFactor.cpp
+++ b/gtsam/discrete/DecisionTreeFactor.cpp
@@ -33,16 +33,13 @@ namespace gtsam {
 
   /* ************************************************************************ */
   DecisionTreeFactor::DecisionTreeFactor(const DiscreteKeys& keys,
-                                        const ADT& potentials)
-      : DiscreteFactor(keys.indices()),
-        ADT(potentials),
-        cardinalities_(keys.cardinalities()) {}
+                                         const ADT& potentials)
+      : DiscreteFactor(keys.indices(), keys.cardinalities()), ADT(potentials) {}
 
   /* ************************************************************************ */
   DecisionTreeFactor::DecisionTreeFactor(const DiscreteConditional& c)
-      : DiscreteFactor(c.keys()),
-        AlgebraicDecisionTree<Key>(c),
-        cardinalities_(c.cardinalities_) {}
+      : DiscreteFactor(c.keys(), c.cardinalities()),
+        AlgebraicDecisionTree<Key>(c) {}
 
   /* ************************************************************************ */
   bool DecisionTreeFactor::equals(const DiscreteFactor& other,
@@ -190,18 +187,6 @@ namespace gtsam {
     return probs;
   }
 
-  /* ************************************************************************ */
-  DiscreteKeys DecisionTreeFactor::discreteKeys() const {
-    DiscreteKeys result;
-    for (auto&& key : keys()) {
-      DiscreteKey dkey(key, cardinality(key));
-      if (std::find(result.begin(), result.end(), dkey) == result.end()) {
-        result.push_back(dkey);
-      }
-    }
-    return result;
-  }
-
   /* ************************************************************************ */
   static std::string valueFormatter(const double& v) {
     std::stringstream ss;
@@ -297,17 +282,15 @@ namespace gtsam {
 
   /* ************************************************************************ */
   DecisionTreeFactor::DecisionTreeFactor(const DiscreteKeys& keys,
-                                        const vector<double>& table)
-      : DiscreteFactor(keys.indices()),
-        AlgebraicDecisionTree<Key>(keys, table),
-        cardinalities_(keys.cardinalities()) {}
+                                         const vector<double>& table)
+      : DiscreteFactor(keys.indices(), keys.cardinalities()),
+        AlgebraicDecisionTree<Key>(keys, table) {}
 
   /* ************************************************************************ */
   DecisionTreeFactor::DecisionTreeFactor(const DiscreteKeys& keys,
-                                        const string& table)
-      : DiscreteFactor(keys.indices()),
-        AlgebraicDecisionTree<Key>(keys, table),
-        cardinalities_(keys.cardinalities()) {}
+                                         const string& table)
+      : DiscreteFactor(keys.indices(), keys.cardinalities()),
+        AlgebraicDecisionTree<Key>(keys, table) {}
 
   /* ************************************************************************ */
   DecisionTreeFactor DecisionTreeFactor::prune(size_t maxNrAssignments) const {
diff --git a/gtsam/discrete/DecisionTreeFactor.h b/gtsam/discrete/DecisionTreeFactor.h
index 42639095f..6cce6e5d4 100644
--- a/gtsam/discrete/DecisionTreeFactor.h
+++ b/gtsam/discrete/DecisionTreeFactor.h
@@ -50,10 +50,6 @@ namespace gtsam {
     typedef std::shared_ptr<DecisionTreeFactor> shared_ptr;
     typedef AlgebraicDecisionTree<Key> ADT;
 
-   protected:
-    std::map<Key, size_t> cardinalities_;
-
-   public:
     /// @name Standard Constructors
     /// @{
 
@@ -119,10 +115,6 @@ namespace gtsam {
 
     static double safe_div(const double& a, const double& b);
 
-    std::map<Key, size_t> cardinalities() const { return cardinalities_; }
-
-    size_t cardinality(Key j) const { return cardinalities_.at(j); }
-
     /// divide by factor f (safely)
     DecisionTreeFactor operator/(const DecisionTreeFactor& f) const {
       return apply(f, safe_div);
@@ -184,9 +176,6 @@ namespace gtsam {
     /// Get all the probabilities in order of assignment values
     std::vector<double> probabilities() const;
 
-    /// Return all the discrete keys associated with this factor.
-    DiscreteKeys discreteKeys() const;
-
     /**
      * @brief Prune the decision tree of discrete variables.
      *
@@ -265,7 +254,6 @@ namespace gtsam {
     void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
       ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
       ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(ADT);
-      ar& BOOST_SERIALIZATION_NVP(cardinalities_);
     }
 #endif
   };
diff --git a/gtsam/discrete/DiscreteFactor.cpp b/gtsam/discrete/DiscreteFactor.cpp
index 2b1bc36a3..b44d4fce2 100644
--- a/gtsam/discrete/DiscreteFactor.cpp
+++ b/gtsam/discrete/DiscreteFactor.cpp
@@ -28,6 +28,18 @@ using namespace std;
 
 namespace gtsam {
 
+/* ************************************************************************ */
+DiscreteKeys DiscreteFactor::discreteKeys() const {
+  DiscreteKeys result;
+  for (auto&& key : keys()) {
+    DiscreteKey dkey(key, cardinality(key));
+    if (std::find(result.begin(), result.end(), dkey) == result.end()) {
+      result.push_back(dkey);
+    }
+  }
+  return result;
+}
+
 /* ************************************************************************* */
 double DiscreteFactor::error(const DiscreteValues& values) const {
   return -std::log((*this)(values));
diff --git a/gtsam/discrete/DiscreteFactor.h b/gtsam/discrete/DiscreteFactor.h
index 2132e1cc8..24b2b55e4 100644
--- a/gtsam/discrete/DiscreteFactor.h
+++ b/gtsam/discrete/DiscreteFactor.h
@@ -45,6 +45,10 @@ class GTSAM_EXPORT DiscreteFactor: public Factor {
 
   using Values = DiscreteValues;  ///< backwards compatibility
 
+ protected:
+  /// Map of Keys and their cardinalities.
+  std::map<Key, size_t> cardinalities_;
+
  public:
   /// @name Standard Constructors
   /// @{
@@ -52,10 +56,15 @@ class GTSAM_EXPORT DiscreteFactor: public Factor {
   /** Default constructor creates empty factor */
   DiscreteFactor() {}
 
-  /** Construct from container of keys.  This constructor is used internally from derived factor
-   *  constructors, either from a container of keys or from a boost::assign::list_of. */
-  template<typename CONTAINER>
-  DiscreteFactor(const CONTAINER& keys) : Base(keys) {}
+  /**
+   * Construct from container of keys and map of cardinalities.
+   * This constructor is used internally from derived factor constructors,
+   * either from a container of keys or from a boost::assign::list_of.
+   */
+  template <typename CONTAINER>
+  DiscreteFactor(const CONTAINER& keys,
+                 const std::map<Key, size_t> cardinalities = {})
+      : Base(keys), cardinalities_(cardinalities) {}
 
   /// @}
   /// @name Testable
@@ -75,6 +84,13 @@ class GTSAM_EXPORT DiscreteFactor: public Factor {
   /// @name Standard Interface
   /// @{
 
+  /// Return all the discrete keys associated with this factor.
+  DiscreteKeys discreteKeys() const;
+
+  std::map<Key, size_t> cardinalities() const { return cardinalities_; }
+
+  size_t cardinality(Key j) const { return cardinalities_.at(j); }
+
   /// Find value for given assignment of values to variables
   virtual double operator()(const DiscreteValues&) const = 0;
 
@@ -130,6 +146,7 @@ class GTSAM_EXPORT DiscreteFactor: public Factor {
   template <class ARCHIVE>
   void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
     ar& BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base);
+    ar& BOOST_SERIALIZATION_NVP(cardinalities_);
   }
 #endif
 };
diff --git a/gtsam/discrete/TableFactor.cpp b/gtsam/discrete/TableFactor.cpp
index c59b7b72c..74eb3ddb3 100644
--- a/gtsam/discrete/TableFactor.cpp
+++ b/gtsam/discrete/TableFactor.cpp
@@ -34,8 +34,7 @@ TableFactor::TableFactor() {}
 /* ************************************************************************ */
 TableFactor::TableFactor(const DiscreteKeys& dkeys,
                          const TableFactor& potentials)
-    : DiscreteFactor(dkeys.indices()),
-      cardinalities_(potentials.cardinalities_) {
+    : DiscreteFactor(dkeys.indices(), dkeys.cardinalities()) {
   sparse_table_ = potentials.sparse_table_;
   denominators_ = potentials.denominators_;
   sorted_dkeys_ = discreteKeys();
@@ -45,11 +44,11 @@ TableFactor::TableFactor(const DiscreteKeys& dkeys,
 /* ************************************************************************ */
 TableFactor::TableFactor(const DiscreteKeys& dkeys,
                          const Eigen::SparseVector<double>& table)
-    : DiscreteFactor(dkeys.indices()), sparse_table_(table.size()) {
+    : DiscreteFactor(dkeys.indices(), dkeys.cardinalities()),
+      sparse_table_(table.size()) {
   sparse_table_ = table;
   double denom = table.size();
   for (const DiscreteKey& dkey : dkeys) {
-    cardinalities_.insert(dkey);
     denom /= dkey.second;
     denominators_.insert(std::pair<Key, double>(dkey.first, denom));
   }
@@ -440,18 +439,6 @@ std::vector<std::pair<DiscreteValues, double>> TableFactor::enumerate() const {
   return result;
 }
 
-/* ************************************************************************ */
-DiscreteKeys TableFactor::discreteKeys() const {
-  DiscreteKeys result;
-  for (auto&& key : keys()) {
-    DiscreteKey dkey(key, cardinality(key));
-    if (std::find(result.begin(), result.end(), dkey) == result.end()) {
-      result.push_back(dkey);
-    }
-  }
-  return result;
-}
-
 // Print out header.
 /* ************************************************************************ */
 string TableFactor::markdown(const KeyFormatter& keyFormatter,
diff --git a/gtsam/discrete/TableFactor.h b/gtsam/discrete/TableFactor.h
index 08c675b67..bd637bb7d 100644
--- a/gtsam/discrete/TableFactor.h
+++ b/gtsam/discrete/TableFactor.h
@@ -45,8 +45,6 @@ class HybridValues;
  */
 class GTSAM_EXPORT TableFactor : public DiscreteFactor {
  protected:
-  /// Map of Keys and their cardinalities.
-  std::map<Key, size_t> cardinalities_;
   /// SparseVector of nonzero probabilities.
   Eigen::SparseVector<double> sparse_table_;
 
@@ -184,8 +182,6 @@ class GTSAM_EXPORT TableFactor : public DiscreteFactor {
 
   static double safe_div(const double& a, const double& b);
 
-  size_t cardinality(Key j) const { return cardinalities_.at(j); }
-
   /// divide by factor f (safely)
   TableFactor operator/(const TableFactor& f) const {
     return apply(f, safe_div);
@@ -278,9 +274,6 @@ class GTSAM_EXPORT TableFactor : public DiscreteFactor {
   /// Enumerate all values into a map from values to double.
   std::vector<std::pair<DiscreteValues, double>> enumerate() const;
 
-  /// Return all the discrete keys associated with this factor.
-  DiscreteKeys discreteKeys() const;
-
   /**
    * @brief Prune the decision tree of discrete variables.
    *