diff --git a/gtsam/discrete/DiscreteFactorGraph.cpp b/gtsam/discrete/DiscreteFactorGraph.cpp
index a166fdce9..7c03d21f9 100644
--- a/gtsam/discrete/DiscreteFactorGraph.cpp
+++ b/gtsam/discrete/DiscreteFactorGraph.cpp
@@ -131,36 +131,39 @@ namespace gtsam {
   }
 
   /* ************************************************************************ */
+  // The max-product solution below is a bit clunky: the elimination machinery
+  // does not allow for differently *typed* versions of elimination, so we
+  // eliminate into a Bayes Net using the special eliminate function above, and
+  // then create the DiscreteLookupDAG after the fact, in linear time.
+
   DiscreteLookupDAG DiscreteFactorGraph::maxProduct(
       OptionalOrderingType orderingType) const {
     gttic(DiscreteFactorGraph_maxProduct);
-
-    // The solution below is a bitclunky: the elimination machinery does not
-    // allow for differently *typed* versions of elimination, so we eliminate
-    // into a Bayes Net using the special eliminate function above, and then
-    // create the DiscreteLookupDAG after the fact, in linear time.
     auto bayesNet =
         BaseEliminateable::eliminateSequential(orderingType, EliminateForMPE);
+    return DiscreteLookupDAG::FromBayesNet(*bayesNet);
+  }
 
-    // Copy to the DAG
-    DiscreteLookupDAG dag;
-    for (auto&& conditional : *bayesNet) {
-      if (auto lookupTable =
-              boost::dynamic_pointer_cast<DiscreteLookupTable>(conditional)) {
-        dag.push_back(lookupTable);
-      } else {
-        throw std::runtime_error(
-            "DiscreteFactorGraph::maxProduct: Expected look up table.");
-      }
-    }
-    return dag;
+  DiscreteLookupDAG DiscreteFactorGraph::maxProduct(
+      const Ordering& ordering) const {
+    gttic(DiscreteFactorGraph_maxProduct);
+    auto bayesNet =
+        BaseEliminateable::eliminateSequential(ordering, EliminateForMPE);
+    return DiscreteLookupDAG::FromBayesNet(*bayesNet);
   }
 
   /* ************************************************************************ */
   DiscreteValues DiscreteFactorGraph::optimize(
       OptionalOrderingType orderingType) const {
     gttic(DiscreteFactorGraph_optimize);
-    DiscreteLookupDAG dag = maxProduct();
+    DiscreteLookupDAG dag = maxProduct(orderingType);
+    return dag.argmax();
+  }
+
+  DiscreteValues DiscreteFactorGraph::optimize(
+      const Ordering& ordering) const {
+    gttic(DiscreteFactorGraph_optimize);
+    DiscreteLookupDAG dag = maxProduct(ordering);
     return dag.argmax();
   }
 
diff --git a/gtsam/discrete/DiscreteFactorGraph.h b/gtsam/discrete/DiscreteFactorGraph.h
index 7c658f548..59827f9a5 100644
--- a/gtsam/discrete/DiscreteFactorGraph.h
+++ b/gtsam/discrete/DiscreteFactorGraph.h
@@ -138,6 +138,14 @@ class GTSAM_EXPORT DiscreteFactorGraph
   DiscreteLookupDAG maxProduct(
       OptionalOrderingType orderingType = boost::none) const;
 
+  /**
+   * @brief Implement the max-product algorithm
+   *
+   * @param ordering
+   * @return DiscreteLookupDAG::shared_ptr `DAG with lookup tables
+   */
+  DiscreteLookupDAG maxProduct(const Ordering& ordering) const;
+
   /**
    * @brief Find the maximum probable explanation (MPE) by doing max-product.
    *
@@ -147,6 +155,14 @@ class GTSAM_EXPORT DiscreteFactorGraph
   DiscreteValues optimize(
       OptionalOrderingType orderingType = boost::none) const;
 
+  /**
+   * @brief Find the maximum probable explanation (MPE) by doing max-product.
+   *
+   * @param ordering
+   * @return DiscreteValues : MPE
+   */
+  DiscreteValues optimize(const Ordering& ordering) const;
+
   //  /** Permute the variables in the factors */
   //  GTSAM_EXPORT void permuteWithInverse(const Permutation&
   //  inversePermutation);
diff --git a/gtsam/discrete/DiscreteLookupDAG.cpp b/gtsam/discrete/DiscreteLookupDAG.cpp
index 1edf508a1..16620cc24 100644
--- a/gtsam/discrete/DiscreteLookupDAG.cpp
+++ b/gtsam/discrete/DiscreteLookupDAG.cpp
@@ -16,6 +16,7 @@
  *  @author Frank Dellaert
  */
 
+#include <gtsam/discrete/DiscreteBayesNet.h>
 #include <gtsam/discrete/DiscreteLookupDAG.h>
 #include <gtsam/discrete/DiscreteValues.h>
 
@@ -99,6 +100,22 @@ size_t DiscreteLookupTable::argmax(const DiscreteValues& parentsValues) const {
   return mpe;
 }
 
+/* ************************************************************************** */
+DiscreteLookupDAG DiscreteLookupDAG::FromBayesNet(
+    const DiscreteBayesNet& bayesNet) {
+  DiscreteLookupDAG dag;
+  for (auto&& conditional : bayesNet) {
+    if (auto lookupTable =
+            boost::dynamic_pointer_cast<DiscreteLookupTable>(conditional)) {
+      dag.push_back(lookupTable);
+    } else {
+      throw std::runtime_error(
+          "DiscreteFactorGraph::maxProduct: Expected look up table.");
+    }
+  }
+  return dag;
+}
+
 /* ************************************************************************** */
 DiscreteValues DiscreteLookupDAG::argmax() const {
   DiscreteValues result;
diff --git a/gtsam/discrete/DiscreteLookupDAG.h b/gtsam/discrete/DiscreteLookupDAG.h
index 1b3a38b40..f1eb24ec3 100644
--- a/gtsam/discrete/DiscreteLookupDAG.h
+++ b/gtsam/discrete/DiscreteLookupDAG.h
@@ -28,6 +28,8 @@
 
 namespace gtsam {
 
+class DiscreteBayesNet;
+
 /**
  * @brief DiscreteLookupTable table for max-product
  *
@@ -83,6 +85,9 @@ class GTSAM_EXPORT DiscreteLookupDAG : public BayesNet<DiscreteLookupTable> {
   /// Construct empty DAG.
   DiscreteLookupDAG() {}
 
+  // Create from BayesNet with LookupTables
+  static DiscreteLookupDAG FromBayesNet(const DiscreteBayesNet& bayesNet);
+
   /// Destructor
   virtual ~DiscreteLookupDAG() {}