diff --git a/gtsam/discrete/AlgebraicDecisionTree.h b/gtsam/discrete/AlgebraicDecisionTree.h
index acdbf63a3..72ea5e79f 100644
--- a/gtsam/discrete/AlgebraicDecisionTree.h
+++ b/gtsam/discrete/AlgebraicDecisionTree.h
@@ -108,9 +108,12 @@ namespace gtsam {
     /** Convert */
     template<typename M>
     AlgebraicDecisionTree(const AlgebraicDecisionTree<M>& other,
-        const std::map<M, L>& map) {
-      this->root_ = this->template convert<M, double>(other.root_, map,
-          Ring::id);
+                          const std::map<M, L>& map) {
+      std::function<L(const M&)> map_function = [&map](const M& label) -> L {
+        return map.at(label);
+      };
+      std::function<double(const double&)> op = Ring::id;
+      this->root_ = this->template convert(other.root_, op, map_function);
     }
 
     /** sum */
diff --git a/gtsam/discrete/DecisionTree-inl.h b/gtsam/discrete/DecisionTree-inl.h
index 209c2ad80..96f1421ce 100644
--- a/gtsam/discrete/DecisionTree-inl.h
+++ b/gtsam/discrete/DecisionTree-inl.h
@@ -453,20 +453,24 @@ namespace gtsam {
     root_ = compose(functions.begin(), functions.end(), label);
   }
 
-  /*********************************************************************************/
-  template<typename L, typename Y>
-  template<typename M, typename X>
-  DecisionTree<L, Y>::DecisionTree(const DecisionTree<M, X>& other,
-      const std::map<M, L>& map, std::function<Y(const X&)> op)  {
-    root_ = convert(other.root_, map, op);
-  }
-
   /*********************************************************************************/
   template <typename L, typename Y>
   template <typename X>
   DecisionTree<L, Y>::DecisionTree(const DecisionTree<L, X>& other,
                                    std::function<Y(const X&)> op) {
-    root_ = convert(other.root_, op);
+    auto map = [](const L& label) { return label; };
+    root_ = convert<L, X>(other.root_, op, map);
+  }
+
+  /*********************************************************************************/
+  template<typename L, typename Y>
+  template<typename M, typename X>
+  DecisionTree<L, Y>::DecisionTree(const DecisionTree<M, X>& other,
+      const std::map<M, L>& map, std::function<Y(const X&)> op)  {
+    std::function<L(const M&)> map_function = [&map](const M& label) -> L {
+      return map.at(label);
+    };
+    root_ = convert<M, X>(other.root_, op, map_function);
   }
 
   /*********************************************************************************/
@@ -579,12 +583,11 @@ namespace gtsam {
   }
 
   /*********************************************************************************/
-  template<typename L, typename Y>
-  template<typename M, typename X>
+  template <typename L, typename Y>
+  template <typename M, typename X>
   typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::convert(
-      const typename DecisionTree<M, X>::NodePtr& f, const std::map<M, L>& map,
-      std::function<Y(const X&)> op) {
-
+      const typename DecisionTree<M, X>::NodePtr& f,
+      std::function<Y(const X&)> op, std::function<L(const M&)> map) {
     typedef DecisionTree<M, X> MX;
     typedef typename MX::Leaf MXLeaf;
     typedef typename MX::Choice MXChoice;
@@ -602,50 +605,18 @@ namespace gtsam {
         "DecisionTree::Convert: Invalid NodePtr");
 
     // get new label
-    M oldLabel = choice->label();
-    L newLabel = map.at(oldLabel);
+    const M oldLabel = choice->label();
+    const L newLabel = map(oldLabel);
 
     // put together via Shannon expansion otherwise not sorted.
     std::vector<LY> functions;
     for(const MXNodePtr& branch: choice->branches()) {
-      LY converted(convert<M, X>(branch, map, op));
+      LY converted(convert<M, X>(branch, op, map));
       functions += converted;
     }
     return LY::compose(functions.begin(), functions.end(), newLabel);
   }
 
-  /*********************************************************************************/
-  template<typename L, typename Y>
-  template<typename X>
-  typename DecisionTree<L, Y>::NodePtr DecisionTree<L, Y>::convert(
-      const typename DecisionTree<L, X>::NodePtr& f,
-      std::function<Y(const X&)> op) {
-
-    typedef DecisionTree<L, X> LX;
-    typedef typename LX::Leaf LXLeaf;
-    typedef typename LX::Choice LXChoice;
-    typedef typename LX::NodePtr LXNodePtr;
-    typedef DecisionTree<L, Y> LY;
-
-    // ugliness below because apparently we can't have templated virtual functions
-    // If leaf, apply unary conversion "op" and create a unique leaf
-    const LXLeaf* leaf = dynamic_cast<const LXLeaf*> (f.get());
-    if (leaf) return NodePtr(new Leaf(op(leaf->constant())));
-
-    // Check if Choice
-    boost::shared_ptr<const LXChoice> choice = boost::dynamic_pointer_cast<const LXChoice> (f);
-    if (!choice) throw std::invalid_argument(
-        "DecisionTree::Convert: Invalid NodePtr");
-
-    // put together via Shannon expansion otherwise not sorted.
-    std::vector<LY> functions;
-    for(const LXNodePtr& branch: choice->branches()) {
-      LY converted(convert<X>(branch, op));
-      functions += converted;
-    }
-    return LY::compose(functions.begin(), functions.end(), choice->label());
-  }
-
   /*********************************************************************************/
   template <typename L, typename Y>
   bool DecisionTree<L, Y>::equals(const DecisionTree& other, double tol,
diff --git a/gtsam/discrete/DecisionTree.h b/gtsam/discrete/DecisionTree.h
index 26817bf79..baf2a79fa 100644
--- a/gtsam/discrete/DecisionTree.h
+++ b/gtsam/discrete/DecisionTree.h
@@ -127,15 +127,11 @@ namespace gtsam {
     template<typename It, typename ValueIt>
     NodePtr create(It begin, It end, ValueIt beginY, ValueIt endY) const;
 
-    /** Convert to a different type */
-    template<typename M, typename X> NodePtr
-    convert(const typename DecisionTree<M, X>::NodePtr& f, const std::map<M,
-        L>& map, std::function<Y(const X&)> op);
-
-    /** Convert only node to a different type */
-    template <typename X>
-    NodePtr convert(const typename DecisionTree<L, X>::NodePtr& f,
-                    const std::function<Y(const X&)> op);
+    /// Convert to a different type, will not convert label if map empty.
+    template <typename M, typename X>
+    NodePtr convert(const typename DecisionTree<M, X>::NodePtr& f,
+                    std::function<Y(const X&)> op,
+                    std::function<L(const M&)> map);
 
    public:
 
@@ -168,16 +164,16 @@ namespace gtsam {
     DecisionTree(const L& label, //
         const DecisionTree& f0, const DecisionTree& f1);
 
-    /** Convert from a different type */
-    template<typename M, typename X>
-    DecisionTree(const DecisionTree<M, X>& other,
-        const std::map<M, L>& map, std::function<Y(const X&)> op);
-
-    /** Convert only nodes from a different type */
+    /** Convert from a different type. */
     template <typename X>
     DecisionTree(const DecisionTree<L, X>& other,
                  std::function<Y(const X&)> op);
 
+    /** Convert from a different type, also transate labels via map. */
+    template<typename M, typename X>
+    DecisionTree(const DecisionTree<M, X>& other,
+        const std::map<M, L>& map, std::function<Y(const X&)> op);
+
     /// @}
     /// @name Testable
     /// @{