diff --git a/ortools/set_cover/set_cover_invariant.cc b/ortools/set_cover/set_cover_invariant.cc
index fbb340e478..36f7653dec 100644
--- a/ortools/set_cover/set_cover_invariant.cc
+++ b/ortools/set_cover/set_cover_invariant.cc
@@ -131,6 +131,25 @@ void SetCoverInvariant::LoadSolution(const SubsetBoolVector& solution) {
   consistency_level_ = CL::kCostAndCoverage;
 }
 
+void SetCoverInvariant::LoadTraceAndCoverage(
+    const std::vector<SetCoverDecision>& trace,
+    const ElementToIntVector& coverage) {
+  ClearRemovabilityInformation();
+  is_selected_.assign(model_->num_subsets(), false);
+  trace_ = trace;
+  coverage_ = coverage;
+  cost_ = 0.0;
+  for (const SetCoverDecision& decision : trace) {
+    if (decision.decision()) {
+      const SubsetIndex subset(decision.subset());
+      is_selected_[subset] = true;
+      cost_ += model_->subset_costs()[subset];
+    }
+  }
+  consistency_level_ = CL::kCostAndCoverage;
+  DCHECK(CheckConsistency(CL::kCostAndCoverage));
+}
+
 bool SetCoverInvariant::NeedToRecompute(ConsistencyLevel cheched_consistency,
                                         ConsistencyLevel target_consistency) {
   return consistency_level_ < cheched_consistency &&
diff --git a/ortools/set_cover/set_cover_invariant.h b/ortools/set_cover/set_cover_invariant.h
index 08ad3d7be7..37e0b8e338 100644
--- a/ortools/set_cover/set_cover_invariant.h
+++ b/ortools/set_cover/set_cover_invariant.h
@@ -165,6 +165,15 @@ class SetCoverInvariant {
   // Loads the solution and recomputes the data in the invariant.
   void LoadSolution(const SubsetBoolVector& solution);
 
+  // Loads the trace and the coverage. When both the trace and the coverage are
+  // loaded, the invariant is consistent at level kCostAndCoverage.
+  // It's also faster than to load a solution and recompute the cost and
+  // coverage. The trace and the coverage are expected to be consistent,
+  // otherwise the behavior is undefined (i.e. the invariant is not consistent,
+  // unless the code is run in DEBUG mode).
+  void LoadTraceAndCoverage(const std::vector<SetCoverDecision>& trace,
+                            const ElementToIntVector& coverage);
+
   // Checks the consistency of the invariant at the given consistency level.
   bool CheckConsistency(ConsistencyLevel consistency) const;
 
diff --git a/ortools/set_cover/set_cover_test.cc b/ortools/set_cover/set_cover_test.cc
index ec52c47298..b9a9c272b2 100644
--- a/ortools/set_cover/set_cover_test.cc
+++ b/ortools/set_cover/set_cover_test.cc
@@ -96,6 +96,7 @@ class KnightsCover {
       const SetCoverInvariant::ConsistencyLevel consistency, int row, int col,
       int radius, SetCoverInvariant* inv) const {
     std::vector<SubsetIndex> cleared_subsets;
+    cleared_subsets.reserve((2 * radius + 1) * (2 * radius + 1));
     for (int r = row - radius; r <= row + radius; ++r) {
       for (int c = col - radius; c <= col + radius; ++c) {
         if (!IsOnBoard(r, c)) continue;
@@ -408,7 +409,8 @@ TEST(SetCoverTest, KnightsCoverElementDegreeRadiusClear) {
   SetCoverModel model = knights.model();
   SetCoverInvariant inv(&model);
   Cost best_cost = std::numeric_limits<Cost>::max();
-  SubsetBoolVector best_choices;
+  std::vector<SetCoverDecision> best_trace;
+  ElementToIntVector best_coverage;
   int iteration = 0;
   for (int radius = 7; radius >= 1; --radius) {
     for (int row = 0; row < BoardSize; ++row) {
@@ -422,11 +424,13 @@ TEST(SetCoverTest, KnightsCoverElementDegreeRadiusClear) {
 
         if (inv.cost() < best_cost) {
           best_cost = inv.cost();
-          best_choices = inv.is_selected();
+          inv.CompressTrace();
+          best_trace = inv.trace();
+          best_coverage = inv.coverage();
           LOG(INFO) << "Best cost: " << best_cost
                     << " at iteration = " << iteration;
         } else {
-          inv.LoadSolution(best_choices);
+          inv.LoadTraceAndCoverage(best_trace, best_coverage);
         }
         knights.ClearSubsetWithinRadius(CL::kCostAndCoverage, row, col, radius,
                                         &inv);
@@ -434,8 +438,8 @@ TEST(SetCoverTest, KnightsCoverElementDegreeRadiusClear) {
       }
     }
   }
-  inv.LoadSolution(best_choices);
-  knights.DisplaySolution(best_choices);
+  inv.LoadTraceAndCoverage(best_trace, best_coverage);
+  knights.DisplaySolution(inv.is_selected());
   LOG(INFO) << "RadiusClear cost: " << best_cost;
   // The best solution found until 2023-08 has a cost of 350.
   // http://www.contestcen.com/kn50.htm