diff --git a/src/test/fuzz/cluster_linearize.cpp b/src/test/fuzz/cluster_linearize.cpp
index 9ce7dbfd7d..4c7906a8b2 100644
--- a/src/test/fuzz/cluster_linearize.cpp
+++ b/src/test/fuzz/cluster_linearize.cpp
@@ -972,27 +972,33 @@ FUZZ_TARGET(clusterlin_simple_linearize)
 
     // If SimpleLinearize claims optimal result, and the cluster is sufficiently small (there are
     // n! linearizations), test that the result is as good as every valid linearization.
-    if (optimal && depgraph.TxCount() <= 7) {
+    if (optimal && depgraph.TxCount() <= 8) {
         std::vector<DepGraphIndex> perm_linearization;
         // Initialize with the lexicographically-first linearization.
         for (DepGraphIndex i : depgraph.Positions()) perm_linearization.push_back(i);
         // Iterate over all valid permutations.
         do {
-            // Determine whether perm_linearization is topological.
+            /** What prefix of perm_linearization is topological. */
+            DepGraphIndex topo_length{0};
             TestBitSet perm_done;
-            bool perm_is_topo{true};
-            for (auto i : perm_linearization) {
+            while (topo_length < perm_linearization.size()) {
+                auto i = perm_linearization[topo_length];
                 perm_done.Set(i);
-                if (!depgraph.Ancestors(i).IsSubsetOf(perm_done)) {
-                    perm_is_topo = false;
-                    break;
-                }
+                if (!depgraph.Ancestors(i).IsSubsetOf(perm_done)) break;
+                ++topo_length;
             }
-            // If so, verify that the obtained linearization is as good as the permutation.
-            if (perm_is_topo) {
+            if (topo_length == perm_linearization.size()) {
+                // If all of perm_linearization is topological, verify that the obtained
+                // linearization is no worse than it.
                 auto perm_chunking = ChunkLinearization(depgraph, perm_linearization);
                 auto cmp = CompareChunks(simple_chunking, perm_chunking);
                 assert(cmp >= 0);
+            } else {
+                // Otherwise, fast forward to the last permutation with the same non-topological
+                // prefix.
+                auto first_non_topo = perm_linearization.begin() + topo_length;
+                assert(std::is_sorted(first_non_topo + 1, perm_linearization.end()));
+                std::reverse(first_non_topo + 1, perm_linearization.end());
             }
         } while(std::next_permutation(perm_linearization.begin(), perm_linearization.end()));
     }