diff --git a/gtsam/discrete/DecisionTree-inl.h b/gtsam/discrete/DecisionTree-inl.h
index 96f1421ce..fbdeae460 100644
--- a/gtsam/discrete/DecisionTree-inl.h
+++ b/gtsam/discrete/DecisionTree-inl.h
@@ -642,6 +642,11 @@ namespace gtsam {
 
   template<typename L, typename Y>
   DecisionTree<L, Y> DecisionTree<L, Y>::apply(const Unary& op) const {
+    // It is unclear what should happen if tree is empty:
+    if (empty()) {
+      throw std::runtime_error(
+          "DecisionTree::apply(unary op) undefined for empty tree.");
+    }
     return DecisionTree(root_->apply(op));
   }
 
@@ -649,6 +654,11 @@ namespace gtsam {
   template<typename L, typename Y>
   DecisionTree<L, Y> DecisionTree<L, Y>::apply(const DecisionTree& g,
       const Binary& op) const {
+    // It is unclear what should happen if either tree is empty:
+    if (empty() or g.empty()) {
+      throw std::runtime_error(
+          "DecisionTree::apply(binary op) undefined for empty trees.");
+    }
     // apply the operaton on the root of both diagrams
     NodePtr h = root_->apply_f_op_g(*g.root_, op);
     // create a new class with the resulting root "h"
diff --git a/gtsam/discrete/DecisionTree.h b/gtsam/discrete/DecisionTree.h
index baf2a79fa..5cf92f157 100644
--- a/gtsam/discrete/DecisionTree.h
+++ b/gtsam/discrete/DecisionTree.h
@@ -194,6 +194,9 @@ namespace gtsam {
     virtual ~DecisionTree() {
     }
 
+    /** empty tree? */
+    bool empty() const { return !root_; }
+
     /** equality */
     bool operator==(const DecisionTree& q) const;
 
diff --git a/gtsam/discrete/tests/testDecisionTree.cpp b/gtsam/discrete/tests/testDecisionTree.cpp
index dbf6cc44b..c7ee6cc2a 100644
--- a/gtsam/discrete/tests/testDecisionTree.cpp
+++ b/gtsam/discrete/tests/testDecisionTree.cpp
@@ -78,6 +78,9 @@ struct Ring {
   static inline int one() {
     return 1;
   }
+  static inline int id(const int& a) {
+    return a;
+  }
   static inline int add(const int& a, const int& b) {
     return a + b;
   }
@@ -100,6 +103,9 @@ TEST(DT, example)
   x10[A] = 1, x10[B] = 0;
   x11[A] = 1, x11[B] = 1;
 
+  // empty
+  DT empty;
+
   // A
   DT a(A, 0, 5);
   LONGS_EQUAL(0,a(x00))
@@ -118,6 +124,11 @@ TEST(DT, example)
   LONGS_EQUAL(5,notb(x10))
   DOT(notb);
 
+  // Check supplying empty trees yields an exception
+  CHECK_EXCEPTION(apply(empty, &Ring::id), std::runtime_error);
+  CHECK_EXCEPTION(apply(empty, a, &Ring::mul), std::runtime_error);
+  CHECK_EXCEPTION(apply(a, empty, &Ring::mul), std::runtime_error);
+
   // apply, two nodes, in natural order
   DT anotb = apply(a, notb, &Ring::mul);
   LONGS_EQUAL(0,anotb(x00))