diff --git a/gtsam/discrete/AlgebraicDecisionTree.h b/gtsam/discrete/AlgebraicDecisionTree.h
index 9cc55ed6a..3469ac5cf 100644
--- a/gtsam/discrete/AlgebraicDecisionTree.h
+++ b/gtsam/discrete/AlgebraicDecisionTree.h
@@ -30,6 +30,13 @@ namespace gtsam {
   template<typename L>
   class AlgebraicDecisionTree: public DecisionTree<L, double> {
 
+    /**
+     * @brief Default method for comparison of two doubles upto some tolerance.
+     */
+    static bool DefaultComparator(double a, double b, double tol) {
+      return std::abs(a - b) < tol;
+    }
+
   public:
 
     typedef DecisionTree<L, double> Super;
@@ -138,6 +145,12 @@ namespace gtsam {
       return this->combine(labelC, &Ring::add);
     }
 
+    /// Equality method customized to node type `double`.
+    bool equals(const AlgebraicDecisionTree& other, double tol = 1e-9,
+                const std::function<bool(double, double, double)>& comparator =
+                    &DefaultComparator) const {
+      return this->root_->equals(*other.root_, tol, comparator);
+    }
   };
 // AlgebraicDecisionTree
 
diff --git a/gtsam/discrete/DecisionTree-inl.h b/gtsam/discrete/DecisionTree-inl.h
index ec6222fd7..f531e2b98 100644
--- a/gtsam/discrete/DecisionTree-inl.h
+++ b/gtsam/discrete/DecisionTree-inl.h
@@ -20,7 +20,6 @@
 #pragma once
 
 #include <gtsam/base/Testable.h>
-#include <gtsam/base/VectorSpace.h>
 #include <gtsam/discrete/DecisionTree.h>
 
 #include <boost/assign/std/vector.hpp>
@@ -77,33 +76,13 @@ namespace gtsam {
       return (q.isLeaf() && q.sameLeaf(*this));
     }
 
-    /// @{
-    /// SFINAE methods for proper substitution.
-    /** equality for integral types. */
-    template <typename T = Y>
-    typename std::enable_if<std::is_integral<T>::value, bool>::type
-    equals(const T& a, const T& b, double tol) const {
-      return std::abs(double(a - b)) < tol;
-    }
-    /** equality for boost::shared_ptr types. */
-    template <typename T = Y>
-    typename std::enable_if<boost::has_dereference<T>::value, bool>::type
-    equals(const T& a, const T& b, double tol) const {
-      return traits<typename T::element_type>::Equals(*a, *b, tol);
-    }
-    /** equality for all other types. */
-    template <typename T = Y>
-    typename std::enable_if<!boost::has_dereference<T>::value && !std::is_integral<T>::value, bool>::type
-    equals(const Y& a, const Y& b, double tol) const {
-      return traits<Y>::Equals(a, b, tol);
-    }
-    /// @}
-
     /** equality up to tolerance */
-    bool equals(const Node& q, double tol) const override {
+    bool equals(const Node& q, double tol,
+                const std::function<bool(const Y&, const Y&, double)>&
+                    comparator) const override {
       const Leaf* other = dynamic_cast<const Leaf*>(&q);
       if (!other) return false;
-      return this->equals<Y>(this->constant_, other->constant_, tol);
+      return comparator(this->constant_, other->constant_, tol);
     }
 
     /** print */
@@ -304,14 +283,17 @@ namespace gtsam {
     }
 
     /** equality up to tolerance */
-    bool equals(const Node& q, double tol) const override {
-      const Choice* other = dynamic_cast<const Choice*> (&q);
+    bool equals(const Node& q, double tol,
+                const std::function<bool(const Y&, const Y&, double)>&
+                    comparator) const override {
+      const Choice* other = dynamic_cast<const Choice*>(&q);
       if (!other) return false;
       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
       for (size_t i = 0; i < branches_.size(); i++)
-        if (!(branches_[i]->equals(*(other->branches_[i]), tol))) return false;
+        if (!(branches_[i]->equals(*(other->branches_[i]), tol, comparator)))
+          return false;
       return true;
     }
 
@@ -668,9 +650,11 @@ namespace gtsam {
   }
 
   /*********************************************************************************/
-  template<typename L, typename Y>
-  bool DecisionTree<L, Y>::equals(const DecisionTree& other, double tol) const {
-    return root_->equals(*other.root_, tol);
+  template <typename L, typename Y>
+  bool DecisionTree<L, Y>::equals(
+      const DecisionTree& other, double tol,
+      const std::function<bool(const Y&, const Y&, double)>& comparator) const {
+    return root_->equals(*other.root_, tol, comparator);
   }
 
   template <typename L, typename Y>
diff --git a/gtsam/discrete/DecisionTree.h b/gtsam/discrete/DecisionTree.h
index 498fce5aa..eb23bc5ce 100644
--- a/gtsam/discrete/DecisionTree.h
+++ b/gtsam/discrete/DecisionTree.h
@@ -39,13 +39,18 @@ namespace gtsam {
   template<typename L, typename Y>
   class GTSAM_EXPORT DecisionTree {
 
-    /// default method used by `formatter` when printing.
+    /// Default method used by `formatter` when printing.
     static std::string DefaultFormatter(const L& x) {
       std::stringstream ss;
       ss << x;
       return ss.str();
     }
 
+    /// Default method for comparison of two objects of type Y.
+    static bool DefaultComparator(const Y& a, const Y& b, double tol) {
+      return a == b;
+    }
+
   public:
 
     /** Handy typedefs for unary and binary function types */
@@ -92,7 +97,9 @@ namespace gtsam {
       virtual void dot(std::ostream& os, bool showZero) const = 0;
       virtual bool sameLeaf(const Leaf& q) const = 0;
       virtual bool sameLeaf(const Node& q) const = 0;
-      virtual bool equals(const Node& other, double tol = 1e-9) const = 0;
+      virtual bool equals(const Node& other, double tol = 1e-9,
+                          const std::function<bool(const Y&, const Y&, double)>&
+                              comparator = &DefaultComparator) const = 0;
       virtual const Y& operator()(const Assignment<L>& x) const = 0;
       virtual Ptr apply(const Unary& op) const = 0;
       virtual Ptr apply_f_op_g(const Node&, const Binary&) const = 0;
@@ -178,7 +185,9 @@ namespace gtsam {
                    &DefaultFormatter) const;
 
     // Testable
-    bool equals(const DecisionTree& other, double tol = 1e-9) const;
+    bool equals(const DecisionTree& other, double tol = 1e-9,
+                const std::function<bool(const Y&, const Y&, double)>&
+                    comparator = &DefaultComparator) const;
 
     /// @}
     /// @name Standard Interface
diff --git a/gtsam/discrete/tests/testDecisionTree.cpp b/gtsam/discrete/tests/testDecisionTree.cpp
index 96f503abc..dbf6cc44b 100644
--- a/gtsam/discrete/tests/testDecisionTree.cpp
+++ b/gtsam/discrete/tests/testDecisionTree.cpp
@@ -40,7 +40,19 @@ void dot(const T&f, const string& filename) {
 
 #define DOT(x)(dot(x,#x))
 
-struct Crazy { int a; double b; };
+struct Crazy {
+  int a;
+  double b;
+
+  bool equals(const Crazy& other, double tol = 1e-12) const {
+    return a == other.a && std::abs(b - other.b) < tol;
+  }
+
+  bool operator==(const Crazy& other) const {
+    return this->equals(other);
+  }
+};
+
 typedef DecisionTree<string,Crazy> CrazyDecisionTree; // check that DecisionTree is actually generic (as it pretends to be)
 
 // traits