diff --git a/src/cluster_linearize.h b/src/cluster_linearize.h
index ad6f1a76032..217c4700afe 100644
--- a/src/cluster_linearize.h
+++ b/src/cluster_linearize.h
@@ -250,10 +250,8 @@ public:
         return ret;
     }
 
-    /** Find some connected component within the subset "todo" of this graph.
-     *
-     * Specifically, this finds the connected component which contains the first transaction of
-     * todo (if any).
+    /** Get the connected component within the subset "todo" that contains tx (which must be in
+     *  todo).
      *
      * Two transactions are considered connected if they are both in `todo`, and one is an ancestor
      * of the other in the entire graph (so not just within `todo`), or transitively there is a
@@ -262,10 +260,11 @@ public:
      *
      * Complexity: O(ret.Count()).
      */
-    SetType FindConnectedComponent(const SetType& todo) const noexcept
+    SetType GetConnectedComponent(const SetType& todo, DepGraphIndex tx) const noexcept
     {
-        if (todo.None()) return todo;
-        auto to_add = SetType::Singleton(todo.First());
+        Assume(todo[tx]);
+        Assume(todo.IsSubsetOf(m_used));
+        auto to_add = SetType::Singleton(tx);
         SetType ret;
         do {
             SetType old = ret;
@@ -279,6 +278,19 @@ public:
         return ret;
     }
 
+    /** Find some connected component within the subset "todo" of this graph.
+     *
+     * Specifically, this finds the connected component which contains the first transaction of
+     * todo (if any).
+     *
+     * Complexity: O(ret.Count()).
+     */
+    SetType FindConnectedComponent(const SetType& todo) const noexcept
+    {
+        if (todo.None()) return todo;
+        return GetConnectedComponent(todo, todo.First());
+    }
+
     /** Determine if a subset is connected.
      *
      * Complexity: O(subset.Count()).
diff --git a/src/test/fuzz/cluster_linearize.cpp b/src/test/fuzz/cluster_linearize.cpp
index c7e40a833da..fb4bf3a719f 100644
--- a/src/test/fuzz/cluster_linearize.cpp
+++ b/src/test/fuzz/cluster_linearize.cpp
@@ -446,19 +446,36 @@ FUZZ_TARGET(clusterlin_components)
     // Construct a depgraph.
     SpanReader reader(buffer);
     DepGraph<TestBitSet> depgraph;
+    std::vector<DepGraphIndex> linearization;
     try {
         reader >> Using<DepGraphFormatter>(depgraph);
     } catch (const std::ios_base::failure&) {}
 
     TestBitSet todo = depgraph.Positions();
     while (todo.Any()) {
-        // Find a connected component inside todo.
-        auto component = depgraph.FindConnectedComponent(todo);
+        // Pick a transaction in todo, or nothing.
+        std::optional<DepGraphIndex> picked;
+        {
+            uint64_t picked_num{0};
+            try {
+                reader >> VARINT(picked_num);
+            } catch (const std::ios_base::failure&) {}
+            if (picked_num < todo.Size() && todo[picked_num]) {
+                picked = picked_num;
+            }
+        }
+
+        // Find a connected component inside todo, including picked if any.
+        auto component = picked ? depgraph.GetConnectedComponent(todo, *picked)
+                                : depgraph.FindConnectedComponent(todo);
 
         // The component must be a subset of todo and non-empty.
         assert(component.IsSubsetOf(todo));
         assert(component.Any());
 
+        // If picked was provided, the component must include it.
+        if (picked) assert(component[*picked]);
+
         // If todo is the entire graph, and the entire graph is connected, then the component must
         // be the entire graph.
         if (todo == depgraph.Positions()) {
diff --git a/src/test/fuzz/txgraph.cpp b/src/test/fuzz/txgraph.cpp
index 010c9e951ed..7eabb013e2b 100644
--- a/src/test/fuzz/txgraph.cpp
+++ b/src/test/fuzz/txgraph.cpp
@@ -561,36 +561,23 @@ FUZZ_TARGET(txgraph)
                 std::shuffle(refs.begin(), refs.end(), rng);
                 // Invoke the real function.
                 auto result = real->CountDistinctClusters(refs, use_main);
-                // Build a vector with representatives of the clusters the Refs occur in in the
+                // Build a set with representatives of the clusters the Refs occur in in the
                 // simulated graph. For each, remember the lowest-index transaction SimPos in the
                 // cluster.
-                std::vector<DepGraphIndex> sim_reps;
+                SimTxGraph::SetType sim_reps;
                 for (auto ref : refs) {
                     // Skip Refs that do not occur in the simulated graph.
                     auto simpos = sel_sim.Find(ref);
                     if (simpos == SimTxGraph::MISSING) continue;
-                    // Start with component equal to just the Ref's SimPos.
-                    auto component = SimTxGraph::SetType::Singleton(simpos);
-                    // Keep adding ancestors/descendants of all elements in component until it no
-                    // longer changes.
-                    while (true) {
-                        auto old_component = component;
-                        for (auto i : component) {
-                            component |= sel_sim.graph.Ancestors(i);
-                            component |= sel_sim.graph.Descendants(i);
-                        }
-                        if (component == old_component) break;
-                    }
+                    // Find the component that includes ref.
+                    auto component = sel_sim.graph.GetConnectedComponent(sel_sim.graph.Positions(), simpos);
                     // Remember the lowest-index SimPos in component, as a representative for it.
                     assert(component.Any());
-                    sim_reps.push_back(component.First());
+                    sim_reps.Set(component.First());
                 }
-                // Remove duplicates from sim_reps.
-                std::sort(sim_reps.begin(), sim_reps.end());
-                sim_reps.erase(std::unique(sim_reps.begin(), sim_reps.end()), sim_reps.end());
                 // Compare the number of deduplicated representatives with the value returned by
                 // the real function.
-                assert(result == sim_reps.size());
+                assert(result == sim_reps.Count());
                 break;
             } else if (command-- == 0) {
                 // DoWork.