diff --git a/src/main/scad/puzzlecad/puzzlecad-burr.scad b/src/main/scad/puzzlecad/puzzlecad-burr.scad
index f38d8d0..992b8b5 100644
--- a/src/main/scad/puzzlecad/puzzlecad-burr.scad
+++ b/src/main/scad/puzzlecad/puzzlecad-burr.scad
@@ -267,7 +267,7 @@ module burr_piece_base(burr_spec, test_poly = undef) {
                 
                 // If the facing cell *is* defined but is from a different component, then
                 // we need to render a space-filler.
-                if (lookup3(burr, facing_cell) > 0 && lookup3(burr, facing_cell) != lookup3(burr, cell)) {
+                if (is_nonzero(lookup3(burr, facing_cell)) && lookup3(burr, facing_cell) != lookup3(burr, cell)) {
                     
                     // Space-filler is 2*insets wide in the facing direction, and (scale - 2*insets - bevel/2)
                     // in the orthogonal directions. This ensures that the corners exactly meet the bevel line
@@ -283,9 +283,9 @@ module burr_piece_base(burr_spec, test_poly = undef) {
                 // duplicates.
                 if (face < 5)
                 for (other_face=[face+1:5]) {
-                    if (lookup3(burr, facing_cell) > 0 &&
-                        lookup3(burr, cell + directions[other_face]) > 0 &&
-                        lookup3(burr, facing_cell + directions[other_face]) > 0 &&
+                    if (is_nonzero(lookup3(burr, facing_cell)) &&
+                        is_nonzero(lookup3(burr, cell + directions[other_face])) &&
+                        is_nonzero(lookup3(burr, facing_cell + directions[other_face])) &&
                         ( lookup3(burr, facing_cell) != lookup3(burr, cell) ||
                           lookup3(burr, cell + directions[other_face]) != lookup3(burr, cell) ||
                           lookup3(burr, facing_cell + directions[other_face]) != lookup3(burr, cell)
diff --git a/src/main/scad/puzzlecad/puzzlecad-layout.scad b/src/main/scad/puzzlecad/puzzlecad-layout.scad
index 43742dd..e601170 100644
--- a/src/main/scad/puzzlecad/puzzlecad-layout.scad
+++ b/src/main/scad/puzzlecad/puzzlecad-layout.scad
@@ -172,8 +172,8 @@ function auto_layout_joints(layers, next_joint_letter, z, type) =
 
 function is_joint_location(layers, offset, x, y, z) =
       layers[z][y][x][0] > 0 && layers[z + offset][y][x][0] > 0 &&
-    !(layers[z][y-1][x][0] > 0 && layers[z][y+1][x][0] > 0 && layers[z + offset][y-1][x][0] > 0 && layers[z + offset][y+1][x][0] > 0) &&
-    !(layers[z][y][x-1][0] > 0 && layers[z][y][x+1][0] > 0 && layers[z + offset][y][x-1][0] > 0 && layers[z + offset][y][x+1][0] > 0);
+    !(is_nonzero(layers[z][y-1][x][0]) && is_nonzero(layers[z][y+1][x][0]) && is_nonzero(layers[z + offset][y-1][x][0]) && is_nonzero(layers[z + offset][y+1][x][0])) &&
+    !(is_nonzero(layers[z][y][x-1][0]) && is_nonzero(layers[z][y][x+1][0]) && is_nonzero(layers[z + offset][y][x-1][0]) && is_nonzero(layers[z + offset][y][x+1][0]));
 
 function to_blank_layer(layer) =
     [ for (yslice = layer)
diff --git a/src/main/scad/puzzlecad/puzzlecad-polyhedra.scad b/src/main/scad/puzzlecad/puzzlecad-polyhedra.scad
index 86c7957..0f6a24e 100644
--- a/src/main/scad/puzzlecad/puzzlecad-polyhedra.scad
+++ b/src/main/scad/puzzlecad/puzzlecad-polyhedra.scad
@@ -413,6 +413,7 @@ function has_beveling() =
     !is_undef($burr_bevel_adjustments);
     
 function is_positive_bevel(bevel) =
+    is_undef(bevel) ? undef :
     let (bevel_or_pair = to_2_vector(bevel))
     bevel_or_pair[0] >= 0.01 || bevel_or_pair[1] >= 0.01;
 
diff --git a/src/main/scad/puzzlecad/puzzlecad-util.scad b/src/main/scad/puzzlecad/puzzlecad-util.scad
index e6dca75..7de3695 100644
--- a/src/main/scad/puzzlecad/puzzlecad-util.scad
+++ b/src/main/scad/puzzlecad/puzzlecad-util.scad
@@ -257,6 +257,9 @@ function union_of_number_lists(list1, list2, i = 0, j = 0) =
 
 /***** Misc *****/
 
+// Returns true if x is defined and not equal to 0.
+function is_nonzero(x) = !is_undef(x) && x != 0;
+
 function argmin(list, i = 0, cur_argmin = undef, cur_min = undef) =
       i >= len(list) ? cur_argmin
     : is_undef(cur_argmin) || list[i] < cur_min ? argmin(list, i + 1, i, list[i])