diff --git a/src/Lynx/Model/Game.cs b/src/Lynx/Model/Game.cs
index 0785d31ea..004d239b1 100644
--- a/src/Lynx/Model/Game.cs
+++ b/src/Lynx/Model/Game.cs
@@ -19,7 +19,8 @@ public sealed class Game : IDisposable
     /// <summary>
     /// Indexed by ply
     /// </summary>
-    private readonly Move[] _moveStack;
+    private readonly PlyStackEntry[] _gameStack;
+
     private bool _disposedValue;
 
     public int HalfMovesWithoutCaptureOrPawnMove { get; set; }
@@ -36,7 +37,7 @@ public Game(ReadOnlySpan<char> fen, ReadOnlySpan<char> rawMoves, Span<Range> ran
     {
         Debug.Assert(Constants.MaxNumberMovesInAGame <= 1024, "Need to customized ArrayPool due to desired array size requirements");
         _positionHashHistory = ArrayPool<ulong>.Shared.Rent(Constants.MaxNumberMovesInAGame);
-        _moveStack = ArrayPool<Move>.Shared.Rent(Constants.MaxNumberMovesInAGame);
+        _gameStack = ArrayPool<PlyStackEntry>.Shared.Rent(Constants.MaxNumberMovesInAGame);
 
         var parsedFen = FENParser.ParseFEN(fen);
         CurrentPosition = new Position(parsedFen);
@@ -230,10 +231,19 @@ public void UpdateInitialPosition()
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void PushToMoveStack(int n, Move move) => _moveStack[n + EvaluationConstants.ContinuationHistoryPlyCount] = move;
+    public void UpdateMoveinStack(int n, Move move) => _gameStack[n + EvaluationConstants.ContinuationHistoryPlyCount].Move = move;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public Move ReadMoveFromStack(int n) => _gameStack[n + EvaluationConstants.ContinuationHistoryPlyCount].Move;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public int ReadStaticEvalFromStack(int n) => _gameStack[n].StaticEval;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public int UpdateStaticEvalInStack(int n, int value) => _gameStack[n].StaticEval = value;
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public Move PopFromMoveStack(int n) => _moveStack[n + EvaluationConstants.ContinuationHistoryPlyCount];
+    public ref PlyStackEntry GameStack(int n) => ref _gameStack[n];
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public int PositionHashHistoryLength() => _positionHashHistoryPointer;
@@ -251,7 +261,7 @@ public void UpdateInitialPosition()
 
     public void FreeResources()
     {
-        ArrayPool<Move>.Shared.Return(_moveStack);
+        ArrayPool<PlyStackEntry>.Shared.Return(_gameStack);
         ArrayPool<ulong>.Shared.Return(_positionHashHistory);
 
         CurrentPosition.FreeResources();
diff --git a/src/Lynx/Model/PlyStackEntry.cs b/src/Lynx/Model/PlyStackEntry.cs
new file mode 100644
index 000000000..5465cbd77
--- /dev/null
+++ b/src/Lynx/Model/PlyStackEntry.cs
@@ -0,0 +1,13 @@
+namespace Lynx.Model;
+
+public struct PlyStackEntry
+{
+    public int StaticEval { get; set; }
+
+    public Move Move { get; set; }
+
+    public PlyStackEntry()
+    {
+        StaticEval = int.MaxValue;
+    }
+}
diff --git a/src/Lynx/Search/MoveOrdering.cs b/src/Lynx/Search/MoveOrdering.cs
index c561179ca..16878d71e 100644
--- a/src/Lynx/Search/MoveOrdering.cs
+++ b/src/Lynx/Search/MoveOrdering.cs
@@ -82,7 +82,7 @@ internal int ScoreMove(Move move, int ply, bool isNotQSearch, ShortMove bestMove
 
             if (ply >= 1)
             {
-                var previousMove = Game.PopFromMoveStack(ply - 1);
+                var previousMove = Game.ReadMoveFromStack(ply - 1);
                 Debug.Assert(previousMove != 0);
                 var previousMovePiece = previousMove.Piece();
                 var previousMoveTargetSquare = previousMove.TargetSquare();
@@ -130,7 +130,7 @@ private void UpdateMoveOrderingHeuristicsOnQuietBetaCutoff(int depth, int ply, R
         {
             // 🔍 Continuation history
             // - Counter move history (continuation history, ply - 1)
-            var previousMove = Game.PopFromMoveStack(ply - 1);
+            var previousMove = Game.ReadMoveFromStack(ply - 1);
             Debug.Assert(previousMove != 0);
 
             previousMovePiece = previousMove.Piece();
diff --git a/src/Lynx/Search/NegaMax.cs b/src/Lynx/Search/NegaMax.cs
index b4186d866..4fdb48d60 100644
--- a/src/Lynx/Search/NegaMax.cs
+++ b/src/Lynx/Search/NegaMax.cs
@@ -48,6 +48,8 @@ private int NegaMax(int depth, int ply, int alpha, int beta, bool parentWasNullM
         if (!isRoot)
         {
             (ttScore, ttBestMove, ttElementType, ttRawScore, ttStaticEval) = _tt.ProbeHash(position, depth, ply, alpha, beta);
+
+            // TT cutoffs
             if (!pvNode && ttScore != EvaluationConstants.NoHashEntry)
             {
                 return ttScore;
@@ -67,6 +69,13 @@ private int NegaMax(int depth, int ply, int alpha, int beta, bool parentWasNullM
         // Before any time-consuming operations
         _searchCancellationTokenSource.Token.ThrowIfCancellationRequested();
 
+        // 🔍 Improving heuristic: the current position has a better static evaluation than
+        // the previous evaluation from the same side (ply - 2).
+        // When true, we can:
+        // - Prune more aggressively when evaluation is too high: current position is even getter
+        // - Prune less aggressively when evaluation is low low: uncertainty on how bad the position really is
+        bool improving = false;
+
         bool isInCheck = position.IsInCheck();
         int staticEval = int.MaxValue;
         int phase = int.MaxValue;
@@ -100,6 +109,13 @@ private int NegaMax(int depth, int ply, int alpha, int beta, bool parentWasNullM
                 phase = position.Phase();
             }
 
+            Game.UpdateStaticEvalInStack(ply, staticEval);
+
+            if (ply >= 2)
+            {
+                improving = staticEval > Game.ReadStaticEvalFromStack(ply - 2);
+            }
+
             // From smol.cs
             // ttEvaluation can be used as a better positional evaluation:
             // If the score is outside what the current bounds are, but it did match flag and depth,
@@ -231,7 +247,7 @@ private int NegaMax(int depth, int ply, int alpha, int beta, bool parentWasNullM
             var oldHalfMovesWithoutCaptureOrPawnMove = Game.HalfMovesWithoutCaptureOrPawnMove;
             var canBeRepetition = Game.Update50movesRule(move, isCapture);
             Game.AddToPositionHashHistory(position.UniqueIdentifier);
-            Game.PushToMoveStack(ply, move);
+            Game.UpdateMoveinStack(ply, move);
 
             [MethodImpl(MethodImplOptions.AggressiveInlining)]
             void RevertMove()
@@ -269,7 +285,7 @@ void RevertMove()
                     // 🔍 Late Move Pruning (LMP) - all quiet moves can be pruned
                     // after searching the first few given by the move ordering algorithm
                     if (depth <= Configuration.EngineSettings.LMP_MaxDepth
-                        && moveIndex >= Configuration.EngineSettings.LMP_BaseMovesToTry + (Configuration.EngineSettings.LMP_MovesDepthMultiplier * depth)) // Based on formula suggested by Antares
+                        && moveIndex >= Configuration.EngineSettings.LMP_BaseMovesToTry + (Configuration.EngineSettings.LMP_MovesDepthMultiplier * depth * depth / (improving ? 1 : 2))) // Based on formula suggested by Antares
                     {
                         RevertMove();
                         break;
@@ -486,6 +502,8 @@ public int QuiescenceSearch(int ply, int alpha, int beta)
             ? ttProbeResult.StaticEval
             : position.StaticEvaluation(Game.HalfMovesWithoutCaptureOrPawnMove).Score;
 
+        Game.UpdateStaticEvalInStack(ply, staticEval);
+
         // Beta-cutoff (updating alpha after this check)
         if (staticEval >= beta)
         {
@@ -553,7 +571,7 @@ public int QuiescenceSearch(int ply, int alpha, int beta)
             PrintPreMove(position, ply, move, isQuiescence: true);
 
             // No need to check for threefold or 50 moves repetitions, since we're only searching captures, promotions, and castles
-            Game.PushToMoveStack(ply, move);
+            Game.UpdateMoveinStack(ply, move);
 
 #pragma warning disable S2234 // Arguments should be passed in the same order as the method parameters
             int score = -QuiescenceSearch(ply + 1, -beta, -alpha);