diff --git a/srf/boolean.cpp b/srf/boolean.cpp
index 56797de..4ee97e0 100644
--- a/srf/boolean.cpp
+++ b/srf/boolean.cpp
@@ -56,13 +56,25 @@ SCurve SCurve::MakeCopySplitAgainst(SShell *agnstA, SShell *agnstB,
             // The intersections were generated by intersecting the pwl
             // edge against a surface; so they must be refined to lie
             // exactly on the original curve.
+            il.ClearTags();
             SInter *pi;
             for(pi = il.First(); pi; pi = il.NextAfter(pi)) {
+                if(pi->srf == srfA || pi->srf == srfB) {
+                    // The edge certainly intersects the surfaces that it
+                    // trims (at its endpoints), but those ones don't count.
+                    // They are culled later, but no sense calculating them
+                    // and they will cause numerical problems (since two
+                    // of the three surfaces they're refined to lie on will
+                    // be identical, so the matrix will be singular).
+                    pi->tag = 1;
+                    continue;
+                }
                 double u, v;
                 (pi->srf)->ClosestPointTo(pi->p, &u, &v, false);
                 (pi->srf)->PointOnSurfaces(srfA, srfB, &u, &v);
                 pi->p = (pi->srf)->PointAt(u, v);
             }
+            il.RemoveTagged();
 
             // And now sort them in order along the line. Note that we must
             // do that after refining, in case the refining would make two