diff --git a/src/traces/contour/close_boundaries.js b/src/traces/contour/close_boundaries.js
index ad525edf4a7..60086f8966c 100644
--- a/src/traces/contour/close_boundaries.js
+++ b/src/traces/contour/close_boundaries.js
@@ -58,14 +58,16 @@ module.exports = function(pathinfo, contours) {
                     }
                     break;
                 case '<':
-                    if(contoursValue < boundaryMin) {
+                    if(contoursValue < boundaryMin ||
+                        (!pi0.edgepaths.length && pi0.starts.length && contoursValue === boundaryMin)) {
                         pi0.prefixBoundary = true;
                     }
                     break;
                 case '[]':
                     v1 = Math.min(contoursValue[0], contoursValue[1]);
                     v2 = Math.max(contoursValue[0], contoursValue[1]);
-                    if(v2 < boundaryMin || v1 > boundaryMax) {
+                    if(v2 < boundaryMin || v1 > boundaryMax ||
+                        (!pi0.edgepaths.length && pi0.starts.length && v2 === boundaryMin)) {
                         pi0.prefixBoundary = true;
                     }
                     break;
diff --git a/src/traces/contour/convert_to_constraints.js b/src/traces/contour/convert_to_constraints.js
index eecd7a1214e..418f10b5575 100644
--- a/src/traces/contour/convert_to_constraints.js
+++ b/src/traces/contour/convert_to_constraints.js
@@ -41,6 +41,9 @@ module.exports = function(pathinfo, operation) {
             for(i = 0; i < pi0.paths.length; i++) {
                 pi0.paths[i] = op0(pi0.paths[i]);
             }
+            for(i = 0; i < pi0.starts.length; i++) {
+                pi0.starts[i] = op0(pi0.starts[i]);
+            }
 
             return pathinfo;
         case '][':
@@ -65,10 +68,12 @@ module.exports = function(pathinfo, operation) {
             for(i = 0; i < pi0.edgepaths.length; i++) {
                 pi0.edgepaths[i] = op0(pi0.edgepaths[i]);
             }
-
             for(i = 0; i < pi0.paths.length; i++) {
                 pi0.paths[i] = op0(pi0.paths[i]);
             }
+            for(i = 0; i < pi0.starts.length; i++) {
+                pi0.starts[i] = op0(pi0.starts[i]);
+            }
 
             while(pi1.edgepaths.length) {
                 pi0.edgepaths.push(op1(pi1.edgepaths.shift()));
@@ -76,6 +81,10 @@ module.exports = function(pathinfo, operation) {
             while(pi1.paths.length) {
                 pi0.paths.push(op1(pi1.paths.shift()));
             }
+            while(pi1.starts.length) {
+                pi0.starts.push(op1(pi1.starts.shift()));
+            }
+
             return [pi0];
     }
 };
@@ -83,6 +92,7 @@ module.exports = function(pathinfo, operation) {
 function copyPathinfo(pi) {
     return Lib.extendFlat({}, pi, {
         edgepaths: Lib.extendDeep([], pi.edgepaths),
-        paths: Lib.extendDeep([], pi.paths)
+        paths: Lib.extendDeep([], pi.paths),
+        starts: Lib.extendDeep([], pi.starts)
     });
 }
diff --git a/test/image/baselines/carpet_rounded-off-edgepath-lt.png b/test/image/baselines/carpet_rounded-off-edgepath-lt.png
index a1c690c8e5d..7be8495577e 100644
Binary files a/test/image/baselines/carpet_rounded-off-edgepath-lt.png and b/test/image/baselines/carpet_rounded-off-edgepath-lt.png differ
diff --git a/test/image/baselines/carpet_rounded-off-edgepath.png b/test/image/baselines/carpet_rounded-off-edgepath.png
index 9206ec7f4a5..14b0e71d137 100644
Binary files a/test/image/baselines/carpet_rounded-off-edgepath.png and b/test/image/baselines/carpet_rounded-off-edgepath.png differ
diff --git a/test/image/baselines/contour_constraints_edge_cases.png b/test/image/baselines/contour_constraints_edge_cases.png
index b9847467489..c85b29bba1f 100644
Binary files a/test/image/baselines/contour_constraints_edge_cases.png and b/test/image/baselines/contour_constraints_edge_cases.png differ