diff --git a/include/kaminpar-shm/kaminpar.h b/include/kaminpar-shm/kaminpar.h
index d129ec09..c3fe4126 100644
--- a/include/kaminpar-shm/kaminpar.h
+++ b/include/kaminpar-shm/kaminpar.h
@@ -694,6 +694,9 @@ class Graph {
 
   [[nodiscard]] bool sorted() const;
 
+  void set_level(int level);
+  [[nodiscard]] int level() const;
+
   [[nodiscard]] AbstractGraph *underlying_graph();
   [[nodiscard]] const AbstractGraph *underlying_graph() const;
 
@@ -707,6 +710,7 @@ class Graph {
 
 private:
   std::unique_ptr<AbstractGraph> _underlying_graph;
+  int _level = 0;
 };
 
 [[nodiscard]] Graph compress(
diff --git a/kaminpar-shm/coarsening/abstract_cluster_coarsener.cc b/kaminpar-shm/coarsening/abstract_cluster_coarsener.cc
index 0add8285..2b475f6d 100644
--- a/kaminpar-shm/coarsening/abstract_cluster_coarsener.cc
+++ b/kaminpar-shm/coarsening/abstract_cluster_coarsener.cc
@@ -95,8 +95,7 @@ bool AbstractClusterCoarsener::keep_allocated_memory() const {
   return level() >= _c_ctx.clustering.max_mem_free_coarsening_level;
 }
 
-void AbstractClusterCoarsener::compute_clustering_for_current_graph(
-    StaticArray<NodeID> &clustering
+void AbstractClusterCoarsener::compute_clustering_for_current_graph(StaticArray<NodeID> &clustering
 ) {
   const bool free_allocated_memory = !keep_allocated_memory();
   const NodeWeight total_node_weight = current().total_node_weight();
@@ -174,9 +173,13 @@ void AbstractClusterCoarsener::contract_current_graph_and_push(StaticArray<NodeI
   START_HEAP_PROFILER("Contract graph");
   START_TIMER("Contract graph");
 
-  _hierarchy.push_back(
-      contract_clustering(current(), std::move(clustering), _c_ctx.contraction, _contraction_m_ctx)
-  );
+  _hierarchy.push_back([&] {
+    auto c_graph = contract_clustering(
+        current(), std::move(clustering), _c_ctx.contraction, _contraction_m_ctx
+    );
+    c_graph->get().set_level(level() + 1);
+    return c_graph;
+  }());
 
   auto project_communities = [&](const std::size_t fine_n,
                                  const NodeID *fine_ptr,
diff --git a/kaminpar-shm/datastructures/graph.cc b/kaminpar-shm/datastructures/graph.cc
index f85febc0..97d382c2 100644
--- a/kaminpar-shm/datastructures/graph.cc
+++ b/kaminpar-shm/datastructures/graph.cc
@@ -16,6 +16,7 @@
 namespace kaminpar::shm {
 
 Graph::Graph(std::unique_ptr<AbstractGraph> graph) : _underlying_graph(std::move(graph)) {}
+
 Graph::~Graph() = default;
 
 Graph::Graph(Graph &&) noexcept = default;
@@ -53,6 +54,14 @@ bool Graph::sorted() const {
   return _underlying_graph->sorted();
 }
 
+void Graph::set_level(const int level) {
+  _level = level;
+}
+
+int Graph::level() const {
+  return _level;
+}
+
 AbstractGraph *Graph::underlying_graph() {
   return _underlying_graph.get();
 }
diff --git a/kaminpar-shm/refinement/jet/jet_refiner.cc b/kaminpar-shm/refinement/jet/jet_refiner.cc
index 8d6e150e..06822071 100644
--- a/kaminpar-shm/refinement/jet/jet_refiner.cc
+++ b/kaminpar-shm/refinement/jet/jet_refiner.cc
@@ -37,7 +37,8 @@ template <typename Graph> class JetRefinerImpl {
     SCOPED_TIMER("Jet Refiner");
     SCOPED_TIMER("Initialization");
 
-    const bool is_coarse_level = p_graph.graph().n() < _ctx.partition.n;
+    const bool is_coarse_level = p_graph.graph().level() > 0;
+
     if (is_coarse_level) {
       _num_rounds = _ctx.refinement.jet.num_rounds_on_coarse_level;
       _initial_gain_temp = _ctx.refinement.jet.initial_gain_temp_on_coarse_level;