diff --git a/mesh.cpp b/mesh.cpp
index cea9847..f8772b5 100644
--- a/mesh.cpp
+++ b/mesh.cpp
@@ -476,19 +476,19 @@ void SKdNode::MakeMeshInto(SMesh *m) {
     }
 }
 
-void SKdNode::FindEdgeOn(Vector a, Vector b, int *n, int cnt) {
+void SKdNode::FindEdgeOn(Vector a, Vector b, int *n, int cnt, bool *inter) {
     if(gt && lt) {
         double ac = a.Element(which),
                bc = b.Element(which);
         if(ac < c + KDTREE_EPS ||
            bc < c + KDTREE_EPS)
         {
-            lt->FindEdgeOn(a, b, n, cnt);
+            lt->FindEdgeOn(a, b, n, cnt, inter);
         }
         if(ac > c - KDTREE_EPS ||
            bc > c - KDTREE_EPS)
         {
-            gt->FindEdgeOn(a, b, n, cnt);
+            gt->FindEdgeOn(a, b, n, cnt, inter);
         }
     } else {
         STriangleLl *ll;
@@ -497,12 +497,37 @@ void SKdNode::FindEdgeOn(Vector a, Vector b, int *n, int cnt) {
 
             if(tr->tag == cnt) continue;
             
+            // Test if this triangle matches up with the given edge
             if((a.Equals(tr->b) && b.Equals(tr->a)) ||
                (a.Equals(tr->c) && b.Equals(tr->b)) ||
                (a.Equals(tr->a) && b.Equals(tr->c)))
             {
                 (*n)++;
+            } else if(((a.Equals(tr->a) && b.Equals(tr->b)) ||
+                       (a.Equals(tr->b) && b.Equals(tr->c)) ||
+                       (a.Equals(tr->c) && b.Equals(tr->a))))
+            {
+                // It's an edge of this triangle, okay.
+            } else {
+                // Check for self-intersection
+                Vector n = (tr->Normal()).WithMagnitude(1);
+                double d = (tr->a).Dot(n);
+                double pa = a.Dot(n) - d, pb = b.Dot(n) - d;
+                // It's an intersection if neither point lies in-plane,
+                // and the edge crosses the plane (should handle in-plane
+                // intersections separately but don't yet).
+                if((pa < -LENGTH_EPS || pa > LENGTH_EPS) &&
+                   (pb < -LENGTH_EPS || pb > LENGTH_EPS) &&
+                   (pa*pb < 0))
+                {
+                    // The edge crosses the plane of the triangle; now see if
+                    // it crosses inside the triangle.
+                    if(tr->ContainsPointProjd(b.Minus(a), a)) {
+                        *inter = true;
+                    }
+                }
             }
+
             // Ensure that we don't count this triangle twice if it appears
             // in two buckets of the kd tree.
             tr->tag = cnt;
@@ -510,7 +535,10 @@ void SKdNode::FindEdgeOn(Vector a, Vector b, int *n, int cnt) {
     }
 }
 
-void SKdNode::MakeNakedEdgesInto(SEdgeList *sel) {
+void SKdNode::MakeNakedEdgesInto(SEdgeList *sel, bool *inter, bool *leaky) {
+    if(inter) *inter = false;
+    if(leaky) *leaky = false;
+
     SMesh m;
     ZERO(&m);
     ClearTags();
@@ -526,10 +554,17 @@ void SKdNode::MakeNakedEdgesInto(SEdgeList *sel) {
             Vector b = (j == 0) ? tr->b : ((j == 1)  ? tr->c : tr->a);
 
             int n = 0, nOther = 0;
-            FindEdgeOn(a, b, &n, cnt);
+            bool thisIntersects = false;
+            FindEdgeOn(a, b, &n, cnt, &thisIntersects);
             if(n != 1) {
                 sel->AddEdge(a, b);
+                if(leaky) *leaky = true;
             }
+            if(thisIntersects) {
+                sel->AddEdge(a, b);
+                if(inter) *inter = true;
+            }
+
             cnt++;
         }
     }
diff --git a/polygon.h b/polygon.h
index d8d0a01..feb102a 100644
--- a/polygon.h
+++ b/polygon.h
@@ -219,8 +219,8 @@ public:
     void MakeMeshInto(SMesh *m);
     void ClearTags(void);
     
-    void FindEdgeOn(Vector a, Vector b, int *n, int cnt);
-    void MakeNakedEdgesInto(SEdgeList *sel);
+    void FindEdgeOn(Vector a, Vector b, int *n, int cnt, bool *inter);
+    void MakeNakedEdgesInto(SEdgeList *sel, bool *inter=NULL, bool *leaky=NULL);
 };
 
 #endif
diff --git a/solvespace.cpp b/solvespace.cpp
index 8ff4f6f..23b9a98 100644
--- a/solvespace.cpp
+++ b/solvespace.cpp
@@ -406,15 +406,23 @@ void SolveSpace::MenuAnalyze(int id) {
 
             SMesh *m = &(SS.GetGroup(SS.GW.activeGroup)->runningMesh);
             SKdNode *root = SKdNode::From(m);
-            root->MakeNakedEdgesInto(&(SS.nakedEdges));
+            bool inters, leaks;
+            root->MakeNakedEdgesInto(&(SS.nakedEdges), &inters, &leaks);
             InvalidateGraphics();
 
+            char *intersMsg = inters ?
+                "The mesh is self-intersecting (NOT okay, invalid)." :
+                "The mesh is not self-intersecting (okay, valid).";
+            char *leaksMsg = leaks ?
+                "The mesh has naked edges (NOT okay, invalid)." :
+                "The mesh is watertight (okay, valid).";
+
             if(SS.nakedEdges.l.n == 0) {
-                Error("Zero naked edges; the model is watertight. "
-                      "An exported STL file will be valid.");
+                Message("%s\r\n\r\n%s\r\n\r\nZero problematic edges, good.",
+                    intersMsg, leaksMsg);
             } else {
-                Error("Found %d naked edges, now highlighted.",
-                    SS.nakedEdges.l.n);
+                Error("%s\r\n\r\n%s\r\n\r\n%d problematic edges, bad.",
+                    intersMsg, leaksMsg, SS.nakedEdges.l.n);
             }
             break;
         }