diff --git a/src/groupmesh.cpp b/src/groupmesh.cpp
index 261148df..6d1b2a7a 100644
--- a/src/groupmesh.cpp
+++ b/src/groupmesh.cpp
@@ -416,6 +416,11 @@ void Group::GenerateDisplayItems() {
             }
         }
 
+        // If we render this mesh, we need to know whether it's transparent,
+        // and we'll want all transparent triangles last, to make the depth test
+        // work correctly.
+        displayMesh.PrecomputeTransparency();
+
         displayDirty = false;
     }
 }
diff --git a/src/mesh.cpp b/src/mesh.cpp
index 4231a198..d8bf9591 100644
--- a/src/mesh.cpp
+++ b/src/mesh.cpp
@@ -34,8 +34,6 @@ void SMesh::AddTriangle(STriMeta meta, Vector a, Vector b, Vector c) {
     AddTriangle(&t);
 }
 void SMesh::AddTriangle(const STriangle *st) {
-    RgbaColor color = st->meta.color;
-    if(!color.IsEmpty() && color.alpha != 255) isTransparent = true;
     l.Add(st);
 }
 
@@ -1091,3 +1089,16 @@ void SOutlineList::MakeFromCopyOf(SOutlineList *sol) {
         l.Add(so);
     }
 }
+
+void SMesh::PrecomputeTransparency() {
+    std::sort(l.begin(), l.end(),
+              [&](const STriangle &sta, const STriangle &stb) {
+        RgbaColor colora = sta.meta.color,
+                  colorb = stb.meta.color;
+        bool opaquea = colora.IsEmpty() || colora.alpha == 255,
+             opaqueb = colorb.IsEmpty() || colorb.alpha == 255;
+
+        if(!opaquea || !opaqueb) isTransparent = true;
+        return (opaquea != opaqueb && opaquea == true);
+    });
+}
diff --git a/src/polygon.h b/src/polygon.h
index 2bd0f8ab..072cd9c1 100644
--- a/src/polygon.h
+++ b/src/polygon.h
@@ -276,6 +276,8 @@ public:
     void MakeEdgesInPlaneInto(SEdgeList *sel, Vector n, double d);
     void MakeOutlinesInto(SOutlineList *sol, EdgeKind type);
 
+    void PrecomputeTransparency();
+
     bool IsEmpty() const;
     void RemapFaces(Group *g, int remap);
 
diff --git a/src/srf/surface.cpp b/src/srf/surface.cpp
index a068ead3..21c628e1 100644
--- a/src/srf/surface.cpp
+++ b/src/srf/surface.cpp
@@ -441,7 +441,6 @@ void SSurface::TriangulateInto(SShell *shell, SMesh *sm) {
         for(i = start; i < sm->l.n; i++) {
             STriangle *st = &(sm->l.elem[i]);
             st->meta = meta;
-            if(st->meta.color.alpha != 255) sm->isTransparent = true;
             st->an = NormalAt(st->a.x, st->a.y);
             st->bn = NormalAt(st->b.x, st->b.y);
             st->cn = NormalAt(st->c.x, st->c.y);