diff --git a/OpenNest.Core/CNC/CuttingStrategy/ContourCuttingStrategy.cs b/OpenNest.Core/CNC/CuttingStrategy/ContourCuttingStrategy.cs
index 51296827..e59b4e58 100644
--- a/OpenNest.Core/CNC/CuttingStrategy/ContourCuttingStrategy.cs
+++ b/OpenNest.Core/CNC/CuttingStrategy/ContourCuttingStrategy.cs
@@ -433,6 +433,22 @@ namespace OpenNest.CNC.CuttingStrategy
         private static bool SameVector(Vector a, Vector b) => SameBits(a.X, b.X) && SameBits(a.Y, b.Y);
         private static bool SameBits(double a, double b) => BitConverter.DoubleToInt64Bits(a) == BitConverter.DoubleToInt64Bits(b);
 
+        // ReindexAt starts the contour at the vertex when the entry is within Tolerance.Epsilon of it
+        // (Line/Arc.SplitAt keep the entity whole), so the lead-in must end there too; otherwise the
+        // cut closes at the vertex, short of the entry by that sliver.
+        private static Vector SnapToSplitVertex(Vector point, Entity entity)
+        {
+            var (start, end) = entity switch
+            {
+                Line line => (line.StartPoint, line.EndPoint),
+                Arc arc => (arc.StartPoint(), arc.EndPoint()),
+                _ => (point, point),
+            };
+            if (point.DistanceTo(start) < Tolerance.Epsilon)
+                return start;
+            return point.DistanceTo(end) < Tolerance.Epsilon ? end : point;
+        }
+
         private void EmitContour(
             Program program,
             Shape shape,
@@ -443,6 +459,7 @@ namespace OpenNest.CNC.CuttingStrategy
             Vector? scrapPierce = null
         )
         {
+            point = SnapToSplitVertex(point, entity);
             var contourType = forceType ?? DetectContourType(shape);
             var winding = DetermineWinding(shape);
             var normal = ComputeNormal(point, entity, contourType, winding);
diff --git a/OpenNest.Tests/CuttingPlanning/NearVertexEntryTests.cs b/OpenNest.Tests/CuttingPlanning/NearVertexEntryTests.cs
new file mode 100644
index 00000000..760b41c3
--- /dev/null
+++ b/OpenNest.Tests/CuttingPlanning/NearVertexEntryTests.cs
@@ -0,0 +1,50 @@
+using OpenNest.CNC;
+using OpenNest.CNC.CuttingPlanning;
+using OpenNest.Geometry;
+
+namespace OpenNest.Tests.CuttingPlanning;
+
+/// <summary>
+/// A closest-point entry can land a hair off an entity's vertex. Emission starts the contour
+/// at that vertex (the split keeps the entity whole), so the lead-in must end there too, or
+/// the cut closes short of where it started and replay refuses the whole plate.
+/// </summary>
+public class NearVertexEntryTests
+{
+    private static readonly Vector Center = new(5, 5);
+    private const double Radius = 0.3125;
+
+    // A hole drawn as two half arcs meeting at its top and bottom, inside a square perimeter.
+    private static Program HalfArcHole()
+    {
+        var p = ExplicitContourTests.Square(false);
+        p.MoveTo(Center.X, Center.Y + Radius);
+        p.ArcTo(Center.X, Center.Y - Radius, Center.X, Center.Y, RotationType.CCW);
+        p.ArcTo(Center.X, Center.Y + Radius, Center.X, Center.Y, RotationType.CCW);
+        return p;
+    }
+
+    [Theory]
+    [InlineData(4.1e-6)] // just before the top vertex, at the end of the second arc
+    [InlineData(-4.1e-6)] // just after it, at the start of the first arc
+    public void HoleCutClosesWhereItsLeadInEnds(double angleFromTop)
+    {
+        var prepared = PreparedContours.Capture(HalfArcHole(), ExplicitContourTests.Parameters());
+        var hole = Enumerable.Range(0, prepared.Count).Single(c => c != prepared.PerimeterOrdinal);
+        var approach = Center + new Vector(System.Math.Sin(angleFromTop), System.Math.Cos(angleFromTop)) * 10;
+        var entry = prepared.ClosestEntry(hole, approach);
+        var top = new Vector(Center.X, Center.Y + Radius);
+        Assert.InRange(entry.Point.DistanceTo(top), 1e-6, 1e-5);
+
+        var program = prepared.Emit(new[] { entry, prepared.ClosestEntry(prepared.PerimeterOrdinal, new Vector(0, 0)) });
+        program.Mode = Mode.Absolute;
+        var holeMotions = program.Codes.OfType<Motion>().SkipWhile(m => m is RapidMove)
+            .TakeWhile(m => m is not RapidMove).ToArray();
+
+        // Line lead-in, then the two half arcs back to the lead-in's end.
+        Assert.Equal(3, holeMotions.Length);
+        Assert.True(holeMotions[^1].EndPoint.DistanceTo(holeMotions[0].EndPoint) <= 1e-9,
+            $"cut ends {holeMotions[^1].EndPoint.DistanceTo(holeMotions[0].EndPoint)} from its start");
+        Assert.True(holeMotions[0].EndPoint.DistanceTo(top) <= 1e-9);
+    }
+}