diff --git a/dsc.h b/dsc.h
index 55a6d02..cb5727c 100644
--- a/dsc.h
+++ b/dsc.h
@@ -67,6 +67,7 @@ public:
     Vector Minus(Vector b);
     Vector Negated(void);
     Vector Cross(Vector b);
+    double DirectionCosineWith(Vector b);
     double Dot(Vector b);
     Vector Normal(int which);
     Vector RotatedAbout(Vector orig, Vector axis, double theta);
diff --git a/srf/boolean.cpp b/srf/boolean.cpp
index a27451f..858d1c1 100644
--- a/srf/boolean.cpp
+++ b/srf/boolean.cpp
@@ -322,10 +322,6 @@ void SSurface::EdgeNormalsWithinSurface(Point2d auv, Point2d buv,
     Point2d enuv;
     enuv.x = enxyz.Dot(tu) / tu.MagSquared();
     enuv.y = enxyz.Dot(tv) / tv.MagSquared();
-    // Don't let the magnitude get too tiny at small chord tolerances; we
-    // will otherwise have numerical problems subtracting nearly-equal
-    // numbers.
-    enuv = enuv.WithMagnitude(0.01);
 
     // Compute the inner and outer normals of this edge (within the srf),
     // in xyz space. These are not necessarily antiparallel, if the
diff --git a/srf/raycast.cpp b/srf/raycast.cpp
index 8229197..4fde6e3 100644
--- a/srf/raycast.cpp
+++ b/srf/raycast.cpp
@@ -7,8 +7,9 @@
 //-----------------------------------------------------------------------------
 #include "solvespace.h"
 
-// Dot product tolerance for perpendicular.
-const double SShell::DOTP_TOL = 1e-3;
+// Dot product tolerance for perpendicular; this is on the direction cosine,
+// so it's about 0.001 degrees.
+const double SShell::DOTP_TOL = 1e-5;
 
 extern int FLAG;
 
@@ -394,7 +395,7 @@ void SShell::AllPointsIntersecting(Vector a, Vector b,
 int SShell::ClassifyRegion(Vector edge_n, Vector inter_surf_n,
                            Vector edge_surf_n)
 {
-    double dot = inter_surf_n.Dot(edge_n);
+    double dot = inter_surf_n.DirectionCosineWith(edge_n);
     if(fabs(dot) < DOTP_TOL) {
         // The edge's surface and the edge-on-face surface
         // are coincident. Test the edge's surface normal
@@ -466,7 +467,7 @@ bool SShell::ClassifyEdge(int *indir, int *outdir,
         // TODO, make this use the appropriate curved normals
         double dotp[2];
         for(int i = 0; i < 2; i++) {
-            dotp[i] = edge_n_out.Dot(inter_surf_n[i]);
+            dotp[i] = edge_n_out.DirectionCosineWith(inter_surf_n[i]);
         }
 
         if(fabs(dotp[1]) < DOTP_TOL) {
diff --git a/util.cpp b/util.cpp
index 0df2d76..e066dc9 100644
--- a/util.cpp
+++ b/util.cpp
@@ -362,6 +362,12 @@ double Vector::Dot(Vector b) {
     return (x*b.x + y*b.y + z*b.z);
 }
 
+double Vector::DirectionCosineWith(Vector b) {
+    Vector a = this->WithMagnitude(1);
+    b = b.WithMagnitude(1);
+    return a.Dot(b);
+}
+
 Vector Vector::Normal(int which) {
     Vector n;