diff --git a/pcbnew/zone.cpp b/pcbnew/zone.cpp
index 5e49a71da8..ed725e0b0f 100644
--- a/pcbnew/zone.cpp
+++ b/pcbnew/zone.cpp
@@ -1007,7 +1007,8 @@ bool ZONE::IsIsland( PCB_LAYER_ID aLayer, int aPolyIdx ) const
 }
 
 
-void ZONE::GetInteractingZones( PCB_LAYER_ID aLayer, std::vector<ZONE*>* aZones ) const
+void ZONE::GetInteractingZones( PCB_LAYER_ID aLayer, std::vector<ZONE*>* aSameNetCollidingZones,
+                                std::vector<ZONE*>* aOtherNetIntersectingZones ) const
 {
     int   epsilon = pcbIUScale.mmToIU( 0.001 );
     BOX2I bbox = GetBoundingBox();
@@ -1022,23 +1023,27 @@ void ZONE::GetInteractingZones( PCB_LAYER_ID aLayer, std::vector<ZONE*>* aZones
         if( !candidate->GetLayerSet().test( aLayer ) )
             continue;
 
-        if( candidate->GetIsRuleArea() )
-            continue;
-
-        if( candidate->GetNetCode() != GetNetCode() )
+        if( candidate->GetIsRuleArea() || candidate->IsTeardropArea() )
             continue;
 
         if( !candidate->GetBoundingBox().Intersects( bbox ) )
             continue;
 
-        for( auto iter = m_Poly->CIterate(); iter; iter++ )
+        if( candidate->GetNetCode() == GetNetCode() )
         {
-            if( candidate->m_Poly->Collide( iter.Get(), epsilon ) )
+            for( auto iter = m_Poly->CIterate(); iter; iter++ )
             {
-                aZones->push_back( candidate );
-                break;
+                if( candidate->m_Poly->Collide( iter.Get(), epsilon ) )
+                {
+                    aSameNetCollidingZones->push_back( candidate );
+                    break;
+                }
             }
         }
+        else
+        {
+            aOtherNetIntersectingZones->push_back( candidate );
+        }
     }
 }
 
@@ -1105,9 +1110,6 @@ bool ZONE::BuildSmoothedPoly( SHAPE_POLY_SET& aSmoothedPoly, PCB_LAYER_ID aLayer
                       }
                   };
 
-    std::vector<ZONE*> interactingZones;
-    GetInteractingZones( aLayer, &interactingZones );
-
     SHAPE_POLY_SET* maxExtents = &flattened;
     SHAPE_POLY_SET  withFillets;
 
@@ -1124,11 +1126,34 @@ bool ZONE::BuildSmoothedPoly( SHAPE_POLY_SET& aSmoothedPoly, PCB_LAYER_ID aLayer
         maxExtents = &withFillets;
     }
 
-    for( ZONE* zone : interactingZones )
+    // We now add in the areas of any same-net, intersecting zones.  This keeps us from smoothing
+    // corners at an intersection (which often produces undesired divots between the intersecting
+    // zones -- see #2752).
+    //
+    // After smoothing, we'll subtract back out everything outside of our zone.
+    std::vector<ZONE*> sameNetCollidingZones;
+    std::vector<ZONE*> otherNetIntersectingZones;
+    GetInteractingZones( aLayer, &sameNetCollidingZones, &otherNetIntersectingZones );
+
+    for( ZONE* sameNetZone : sameNetCollidingZones )
     {
-        SHAPE_POLY_SET flattened_outline = zone->Outline()->CloneDropTriangulation();
-        flattened_outline.ClearArcs();
-        aSmoothedPoly.BooleanAdd( flattened_outline, SHAPE_POLY_SET::PM_FAST );
+        BOX2I          sameNetBoundingBox = sameNetZone->GetBoundingBox();
+        SHAPE_POLY_SET sameNetPoly = sameNetZone->Outline()->CloneDropTriangulation();
+
+        sameNetPoly.ClearArcs();
+
+        // Of course there's always a wrinkle.  The same-net intersecting zone *might* get knocked
+        // out along the border by a higher-priority, different-net zone.  #12797
+        for( ZONE* otherNetZone : otherNetIntersectingZones )
+        {
+            if( otherNetZone->HigherPriority( sameNetZone )
+                    && otherNetZone->GetBoundingBox().Intersects( sameNetBoundingBox ) )
+            {
+                sameNetPoly.BooleanSubtract( *otherNetZone->Outline(), SHAPE_POLY_SET::PM_FAST );
+            }
+        }
+
+        aSmoothedPoly.BooleanAdd( sameNetPoly, SHAPE_POLY_SET::PM_FAST );
     }
 
     if( aBoardOutline )
diff --git a/pcbnew/zone.h b/pcbnew/zone.h
index 9ce3085a6a..dbcb1dd9f4 100644
--- a/pcbnew/zone.h
+++ b/pcbnew/zone.h
@@ -352,7 +352,8 @@ public:
      * merged due to other parameters such as fillet radius.  The copper pour will end up
      * effectively merged though, so we need to do some calculations with them in mind.
      */
-    void GetInteractingZones( PCB_LAYER_ID aLayer, std::vector<ZONE*>* aZones ) const;
+    void GetInteractingZones( PCB_LAYER_ID aLayer, std::vector<ZONE*>* aSameNetCollidingZones,
+                              std::vector<ZONE*>* aOtherNetIntersectingZones ) const;
 
     /**
      * Convert solid areas full shapes to polygon set