diff --git a/gtsam_unstable/nonlinear/BayesTreeMarginalizationHelper.h b/gtsam_unstable/nonlinear/BayesTreeMarginalizationHelper.h
index 04e4e0cac..724814fd0 100644
--- a/gtsam_unstable/nonlinear/BayesTreeMarginalizationHelper.h
+++ b/gtsam_unstable/nonlinear/BayesTreeMarginalizationHelper.h
@@ -21,6 +21,7 @@
 #pragma once
 
 #include <unordered_map>
+#include <deque>
 #include <gtsam/inference/BayesTree.h>
 #include <gtsam/inference/BayesTreeCliqueBase.h>
 #include <gtsam/base/debug.h>
@@ -50,9 +51,12 @@ public:
    * 2. Or it has a child node depending on a marginalizable variable AND the
    *    subtree rooted at that child contains non-marginalizables.
    * 
-   * In addition, the subtrees under the aforementioned cliques that require
-   * re-elimination, which contain non-marginalizable variables in their root
-   * node, also need to be re-eliminated.
+   * In addition, for any descendant node depending on a marginalizable
+   * variable, if the subtree rooted at that descendant contains
+   * non-marginalizable variables (i.e., it lies on a path from one of the
+   * aforementioned cliques that require re-elimination to a node containing
+   * non-marginalizable variables at the leaf side), then it also needs to
+   * be re-eliminated.
    * 
    * @param[in] bayesTree The Bayes tree
    * @param[in] marginalizableKeys Keys to be marginalized
@@ -66,7 +70,7 @@ public:
     std::set<Key> additionalKeys;
     std::set<Key> marginalizableKeySet(
         marginalizableKeys.begin(), marginalizableKeys.end());
-    std::set<sharedClique> dependentSubtrees;
+    std::set<sharedClique> dependentCliques;
     CachedSearch cachedSearch;
 
     // Check each clique that contains a marginalizable key
@@ -77,17 +81,14 @@ public:
         // Add frontal variables from current clique
         addCliqueToKeySet(clique, &additionalKeys);
 
-        // Then gather dependent subtrees to be added later
-        gatherDependentSubtrees(
-            clique, marginalizableKeySet, &dependentSubtrees, &cachedSearch);
+        // Then add the dependent cliques
+        for (const sharedClique& dependent :
+             gatherDependentCliques(clique, marginalizableKeySet, &cachedSearch)) {
+          addCliqueToKeySet(dependent, &additionalKeys);
+        }
       }
     }
 
-    // Add the remaining dependent cliques
-    for (const sharedClique& subtree : dependentSubtrees) {
-      addSubtreeToKeySet(subtree, &additionalKeys);
-    }
-
     if (debug) {
       std::cout << "BayesTreeMarginalizationHelper: Additional keys to re-eliminate: ";
       for (const Key& key : additionalKeys) {
@@ -219,53 +220,53 @@ public:
   }
 
   /**
-   * Gather all subtrees that depend on a marginalizable key and contain
-   * non-marginalizable variables in their root.
+   * Gather all dependent nodes that lie on a path from the root clique
+   * to a clique containing a non-marginalizable variable at the leaf side.
    *
-   * @param[in] rootClique The starting clique
+   * @param[in] rootClique The root clique
    * @param[in] marginalizableKeys Set of keys to be marginalized
-   * @param[out] dependentSubtrees Pointer to set storing dependent cliques
    */
-  static void gatherDependentSubtrees(
+  static std::set<sharedClique> gatherDependentCliques(
       const sharedClique& rootClique,
       const std::set<Key>& marginalizableKeys,
-      std::set<sharedClique>* dependentSubtrees,
       CachedSearch* cache) {
-    for (Key key : rootClique->conditional()->frontals()) {
-      if (marginalizableKeys.count(key)) {
-        // Find children that depend on this key
-        for (const sharedClique& child : rootClique->children) {
-          if (!dependentSubtrees->count(child) &&
-              hasDependency(child, key)) {
-            getSubtreesContainingNonMarginalizables(
-                child, marginalizableKeys, cache, dependentSubtrees);
-          }
-        }
+    std::vector<sharedClique> dependentChildren;
+    dependentChildren.reserve(rootClique->children.size());
+    for (const sharedClique& child : rootClique->children) {
+      if (hasDependency(child, marginalizableKeys)) {
+        dependentChildren.push_back(child);
       }
     }
+    return gatherDependentCliquesFromChildren(dependentChildren, marginalizableKeys, cache);
   }
 
   /**
-   * Gather all subtrees that contain non-marginalizable variables in its root.
+   * A helper function for the above gatherDependentCliques().
    */
-  static void getSubtreesContainingNonMarginalizables(
-      const sharedClique& rootClique,
+  static std::set<sharedClique> gatherDependentCliquesFromChildren(
+      const std::vector<sharedClique>& dependentChildren,
       const std::set<Key>& marginalizableKeys,
-      CachedSearch* cache,
-      std::set<sharedClique>* subtreesContainingNonMarginalizables) {
-    // If the root clique itself contains non-marginalizable variables, we
-    // just add it to subtreesContainingNonMarginalizables;    
-    if (!isWholeCliqueMarginalizable(rootClique, marginalizableKeys, cache)) {
-      subtreesContainingNonMarginalizables->insert(rootClique);
-      return;
-    }
+      CachedSearch* cache) {
+    std::deque<sharedClique> descendants(
+        dependentChildren.begin(), dependentChildren.end());
+    std::set<sharedClique> dependentCliques;
+    while (!descendants.empty()) {
+      sharedClique descendant = descendants.front();
+      descendants.pop_front();
 
-    // Otherwise, we need to recursively check the children
-    for (const sharedClique& child : rootClique->children) {
-      getSubtreesContainingNonMarginalizables(
-          child, marginalizableKeys, cache,
-          subtreesContainingNonMarginalizables);
+      // If the subtree rooted at this descendant contains non-marginalizables,
+      // it must lie on a path from the root clique to a clique containing
+      // non-marginalizables at the leaf side.
+      if (!isWholeSubtreeMarginalizable(descendant, marginalizableKeys, cache)) {
+        dependentCliques.insert(descendant);
+      }
+
+      // Add all children of the current descendant to the set descendants.
+      for (const sharedClique& child : descendant->children) {
+        descendants.push_back(child);
+      }
     }
+    return dependentCliques;
   }
 
   /**
@@ -282,28 +283,6 @@ public:
     }
   }
 
-  /**
-   * Add all frontal variables from a subtree to a key set.
-   *
-   * @param[in] subRoot Root clique of the subtree
-   * @param[out] additionalKeys Pointer to the output key set
-   */
-  static void addSubtreeToKeySet(
-      const sharedClique& subRoot,
-      std::set<Key>* additionalKeys) {
-    std::set<sharedClique> cliques;
-    cliques.insert(subRoot);
-    while(!cliques.empty()) {
-      auto begin = cliques.begin();
-      sharedClique clique = *begin;
-      cliques.erase(begin);
-      addCliqueToKeySet(clique, additionalKeys);
-      for (const sharedClique& child : clique->children) {
-        cliques.insert(child);
-      }
-    }
-  }
-
   /**
    * Check if the clique depends on the given key.
    * 
@@ -322,6 +301,19 @@ public:
       return false;
     }
   }
+
+  /**
+   * Check if the clique depends on any of the given keys.
+   */
+  static bool hasDependency(
+      const sharedClique& clique, const std::set<Key>& keys) {
+    for (Key key : keys) {
+      if (hasDependency(clique, key)) {
+        return true;
+      }
+    }
+    return false;
+  }
 };
 // BayesTreeMarginalizationHelper