diff --git a/dsc.h b/dsc.h
index cde82c6..d4cfbf1 100644
--- a/dsc.h
+++ b/dsc.h
@@ -47,7 +47,7 @@ public:
                                          Vector n2, double d2);
 
     double Element(int i);
-    bool Equals(Vector v);
+    bool Equals(Vector v, double tol=LENGTH_EPS);
     bool EqualsExactly(Vector v);
     Vector Plus(Vector b);
     Vector Minus(Vector b);
diff --git a/mesh.cpp b/mesh.cpp
index db8e630..c68ab2f 100644
--- a/mesh.cpp
+++ b/mesh.cpp
@@ -588,9 +588,9 @@ void SKdNode::FindEdgeOn(Vector a, Vector b, int *n, int *nOther,
 
             if(tr->tag == cnt) continue;
             
-            if((a.EqualsExactly(tr->b) && b.EqualsExactly(tr->a)) ||
-               (a.EqualsExactly(tr->c) && b.EqualsExactly(tr->b)) ||
-               (a.EqualsExactly(tr->a) && b.EqualsExactly(tr->c)))
+            if((a.Equals(tr->b, KDTREE_EPS) && b.Equals(tr->a, KDTREE_EPS)) ||
+               (a.Equals(tr->c, KDTREE_EPS) && b.Equals(tr->b, KDTREE_EPS)) ||
+               (a.Equals(tr->a, KDTREE_EPS) && b.Equals(tr->c, KDTREE_EPS)))
             {
                 (*n)++;
                 if(tr->meta.face != m.face) {
@@ -643,7 +643,9 @@ void SKdNode::MakeCertainEdgesInto(SEdgeList *sel, bool emphasized) {
             FindEdgeOn(a, b, &n, &nOther, tr->meta, cnt++);
             if(n != 1) {
                 if(!emphasized) {
-                    if(n == 0) sel->AddEdge(a, b);
+                    if(n == 0 && (a.Minus(b).Magnitude()) > KDTREE_EPS) {
+                        sel->AddEdge(a, b);
+                    }
                 } else {
 //                    dbp("hanging: n=%d (%.3f %.3f %.3f)  (%.3f %.3f %.3f)", 
 //                        n, CO(a), CO(b));
diff --git a/util.cpp b/util.cpp
index be84d64..b28d88d 100644
--- a/util.cpp
+++ b/util.cpp
@@ -290,13 +290,13 @@ double Vector::Element(int i) {
     }
 }
 
-bool Vector::Equals(Vector v) {
+bool Vector::Equals(Vector v, double tol) {
     // Quick axis-aligned tests before going further
-    double dx = v.x - x; if(dx < -LENGTH_EPS || dx > LENGTH_EPS) return false;
-    double dy = v.y - y; if(dy < -LENGTH_EPS || dy > LENGTH_EPS) return false;
-    double dz = v.z - z; if(dz < -LENGTH_EPS || dz > LENGTH_EPS) return false;
+    double dx = v.x - x; if(dx < -tol || dx > tol) return false;
+    double dy = v.y - y; if(dy < -tol || dy > tol) return false;
+    double dz = v.z - z; if(dz < -tol || dz > tol) return false;
 
-    return (this->Minus(v)).MagSquared() < LENGTH_EPS*LENGTH_EPS;
+    return (this->Minus(v)).MagSquared() < tol*tol;
 }
 
 bool Vector::EqualsExactly(Vector v) {