diff --git a/common/geometry/shape_poly_set.cpp b/common/geometry/shape_poly_set.cpp
index 3dd21d32aa..4bb1ea1b59 100644
--- a/common/geometry/shape_poly_set.cpp
+++ b/common/geometry/shape_poly_set.cpp
@@ -1871,27 +1871,23 @@ void SHAPE_POLY_SET::CacheTriangulation()
     m_triangulatedPolys.clear();
     m_triangulationValid = true;
 
-    for( int i = 0; i < tmpSet.OutlineCount(); i++ )
+    while( tmpSet.OutlineCount() > 0 )
     {
         m_triangulatedPolys.push_back( std::make_unique<TRIANGULATED_POLYGON>() );
         PolygonTriangulation tess( *m_triangulatedPolys.back() );
 
         // If the tesselation fails, we re-fracture the polygon, which will
         // first simplify the system before fracturing and removing the holes
-        if( !tess.TesselatePolygon( tmpSet.Polygon( i ).front() ) )
+        // This may result in multiple, disjoint polygons.
+        if( !tess.TesselatePolygon( tmpSet.Polygon( 0 ).front() ) )
         {
             tmpSet.Fracture( PM_FAST );
-
-            // After fracturing, we may have zero or one polygon
-            // Check for zero polygons before tesselating and break regardless
-            if( !tmpSet.OutlineCount() ||  !tess.TesselatePolygon( tmpSet.Polygon( i ).front() ) )
-            {
-                m_triangulatedPolys.pop_back();
-                m_triangulationValid = false;
-            }
-
-            break;
+            m_triangulationValid = false;
+            continue;
         }
+
+        tmpSet.DeletePolygon( 0 );
+        m_triangulationValid = true;
     }
 
     if( m_triangulationValid )
diff --git a/include/geometry/polygon_triangulation.h b/include/geometry/polygon_triangulation.h
index b419b45c6f..c1c0dbfdf7 100644
--- a/include/geometry/polygon_triangulation.h
+++ b/include/geometry/polygon_triangulation.h
@@ -263,9 +263,9 @@ private:
      * as the NULL triangles are inserted as Steiner points to improve the
      * triangulation regularity of polygons
      */
-    bool removeNullTriangles( Vertex* aStart )
+    Vertex* removeNullTriangles( Vertex* aStart )
     {
-        bool retval = false;
+        Vertex* retval = nullptr;
         Vertex* p = aStart->next;
 
         while( p != aStart )
@@ -274,7 +274,7 @@ private:
             {
                 p = p->prev;
                 p->next->remove();
-                retval = true;
+                retval = aStart;
 
                 if( p == p->next )
                     break;
@@ -286,8 +286,8 @@ private:
         // here we do the final check for this as a Steiner point
         if( area( aStart->prev, aStart, aStart->next ) == 0.0 )
         {
+            retval = p->next;
             p->remove();
-            retval = true;
         }
 
         return retval;
@@ -433,8 +433,13 @@ private:
             if( aPoint == stop )
             {
                 // First, try to remove the remaining steiner points
-                if( removeNullTriangles( aPoint ) )
+                // If aPoint is a steiner, we need to re-assign both the start and stop points
+                if( auto newPoint = removeNullTriangles( aPoint ) )
+                {
+                    aPoint = newPoint;
+                    stop = newPoint;
                     continue;
+                }
 
                 // If we don't have any NULL triangles left, cut the polygon in two and try again
                 splitPolygon( aPoint );