diff --git a/gtsam/discrete/discrete.i b/gtsam/discrete/discrete.i
index 5fce25cf5..8bcb8b4aa 100644
--- a/gtsam/discrete/discrete.i
+++ b/gtsam/discrete/discrete.i
@@ -95,10 +95,14 @@ virtual class DiscreteConditional : gtsam::DecisionTreeFactor {
   DiscreteConditional(const gtsam::DecisionTreeFactor& joint,
                       const gtsam::DecisionTreeFactor& marginal,
                       const gtsam::Ordering& orderedKeys);
+  gtsam::DiscreteConditional operator*(
+      const gtsam::DiscreteConditional& other) const;
   void print(string s = "Discrete Conditional\n",
              const gtsam::KeyFormatter& keyFormatter =
                  gtsam::DefaultKeyFormatter) const;
   bool equals(const gtsam::DiscreteConditional& other, double tol = 1e-9) const;
+  size_t nrFrontals() const;
+  size_t nrParents() const;
   void printSignature(
       string s = "Discrete Conditional: ",
       const gtsam::KeyFormatter& formatter = gtsam::DefaultKeyFormatter) const;
diff --git a/python/gtsam/tests/test_DecisionTreeFactor.py b/python/gtsam/tests/test_DecisionTreeFactor.py
index 03d9f82d7..a13a43e26 100644
--- a/python/gtsam/tests/test_DecisionTreeFactor.py
+++ b/python/gtsam/tests/test_DecisionTreeFactor.py
@@ -40,7 +40,7 @@ class TestDecisionTreeFactor(GtsamTestCase):
         prior = DiscretePrior(v1, [1, 3])
         f1 = DecisionTreeFactor([v0, v1], "1 2 3 4")
         expected = DecisionTreeFactor([v0, v1], "0.25 1.5 0.75 3")
-        self.gtsamAssertEquals(prior * f1, expected)
+        self.gtsamAssertEquals(DecisionTreeFactor(prior) * f1, expected)
         self.gtsamAssertEquals(f1 * prior, expected)
 
         # Multiply two factors
diff --git a/python/gtsam/tests/test_DiscreteConditional.py b/python/gtsam/tests/test_DiscreteConditional.py
index 0ae66c2d4..190c22181 100644
--- a/python/gtsam/tests/test_DiscreteConditional.py
+++ b/python/gtsam/tests/test_DiscreteConditional.py
@@ -16,6 +16,13 @@ import unittest
 from gtsam import DecisionTreeFactor, DiscreteConditional, DiscreteKeys
 from gtsam.utils.test_case import GtsamTestCase
 
+# Some DiscreteKeys for binary variables:
+A = 0, 2
+B = 1, 2
+C = 2, 2
+D = 4, 2
+E = 3, 2
+
 
 class TestDiscreteConditional(GtsamTestCase):
     """Tests for Discrete Conditionals."""
@@ -36,6 +43,44 @@ class TestDiscreteConditional(GtsamTestCase):
         actual = conditional.sample(2)
         self.assertIsInstance(actual, int)
 
+    def test_multiply(self):
+        """Check calculation of joint P(A,B)"""
+        conditional = DiscreteConditional(A, [B], "1/2 2/1")
+        prior = DiscreteConditional(B, "1/2")
+
+        # P(A,B) = P(A|B) * P(B) = P(B) * P(A|B)
+        for actual in [prior * conditional, conditional * prior]:
+            self.assertEqual(2, actual.nrFrontals())
+            for v, value in actual.enumerate():
+                self.assertAlmostEqual(actual(v), conditional(v) * prior(v))
+
+    def test_multiply2(self):
+        """Check calculation of conditional joint P(A,B|C)"""
+        A_given_B = DiscreteConditional(A, [B], "1/3 3/1")
+        B_given_C = DiscreteConditional(B, [C], "1/3 3/1")
+
+        # P(A,B|C) = P(A|B)P(B|C) = P(B|C)P(A|B)
+        for actual in [A_given_B * B_given_C, B_given_C * A_given_B]:
+            self.assertEqual(2, actual.nrFrontals())
+            self.assertEqual(1, actual.nrParents())
+            for v, value in actual.enumerate():
+                self.assertAlmostEqual(actual(v), A_given_B(v) * B_given_C(v))
+
+    def test_multiply4(self):
+        """Check calculation of joint P(A,B,C|D,E) = P(A,B|D) P(C|D,E)"""
+        A_given_B = DiscreteConditional(A, [B], "1/3 3/1")
+        B_given_D = DiscreteConditional(B, [D], "1/3 3/1")
+        AB_given_D = A_given_B * B_given_D
+        C_given_DE = DiscreteConditional(C, [D,  E], "4/1 1/1 1/1 1/4")
+
+        # P(A,B,C|D,E) = P(A,B|D) P(C|D,E) = P(C|D,E) P(A,B|D)
+        for actual in [AB_given_D * C_given_DE, C_given_DE * AB_given_D]:
+            self.assertEqual(3, actual.nrFrontals())
+            self.assertEqual(2, actual.nrParents())
+            for v, value in actual.enumerate():
+                self.assertAlmostEqual(
+                    actual(v), AB_given_D(v) * C_given_DE(v))
+
     def test_markdown(self):
         """Test whether the _repr_markdown_ method."""
 
@@ -48,8 +93,7 @@ class TestDiscreteConditional(GtsamTestCase):
 
         conditional = DiscreteConditional(A, parents,
                                           "0/1 1/3  1/1 3/1  0/1 1/0")
-        expected = \
-            " *P(A|B,C):*\n\n" \
+        expected = " *P(A|B,C):*\n\n" \
             "|*B*|*C*|0|1|\n" \
             "|:-:|:-:|:-:|:-:|\n" \
             "|0|0|0|1|\n" \