diff --git a/lib/mayaUsd/ufe/Utils.cpp b/lib/mayaUsd/ufe/Utils.cpp
index f918c7994a..b5675d99e7 100644
--- a/lib/mayaUsd/ufe/Utils.cpp
+++ b/lib/mayaUsd/ufe/Utils.cpp
@@ -162,13 +162,13 @@ std::string uniqueChildNameMayaStandard(const PXR_NS::UsdPrim& usdParent, const
 
         std::string             childBaseName;
         std::pair<TfToken, int> largestMatching("", -1);
-        for (const auto child : allChildrenNames) {
+        for (const auto& child : allChildrenNames) {
             // While iterating thru all the children look for ones that match
             // the base name of the input. When we find one check its numerical
             // suffix and store the greatest one.
             splitNumericalSuffix(child.GetString(), childBaseName, suffix);
             if (baseName == childBaseName) {
-                int suffixValue = std::stoi(suffix);
+                int suffixValue = !suffix.empty() ? std::stoi(suffix) : 0;
                 if (suffixValue > largestMatching.second) {
                     largestMatching = std::make_pair(child, suffixValue);
                 }
diff --git a/lib/usdUfe/python/wrapUtils.cpp b/lib/usdUfe/python/wrapUtils.cpp
index 7c7c795f02..a965b630d6 100644
--- a/lib/usdUfe/python/wrapUtils.cpp
+++ b/lib/usdUfe/python/wrapUtils.cpp
@@ -57,7 +57,10 @@ std::string _usdPathToUfePathSegment(
 
 std::string _uniqueName(const std::vector<std::string>& existingNames, std::string srcName)
 {
-    PXR_NS::TfToken::HashSet existingNamesSet(existingNames.begin(), existingNames.end());
+    PXR_NS::TfToken::HashSet existingNamesSet;
+    for (const auto& n : existingNames) {
+        existingNamesSet.insert(PXR_NS::TfToken(n));
+    }
     return UsdUfe::uniqueName(existingNamesSet, srcName);
 }
 
@@ -77,6 +80,11 @@ int _ufePathToInstanceIndex(const std::string& ufePathString)
     return UsdUfe::ufePathToInstanceIndex(Ufe::PathString::path(ufePathString));
 }
 
+bool _isEditTargetLayerModifiable(const PXR_NS::UsdStageWeakPtr stage)
+{
+    return UsdUfe::isEditTargetLayerModifiable(stage);
+}
+
 PXR_NS::UsdTimeCode _getTime(const std::string& pathStr)
 {
     const Ufe::Path path = Ufe::PathString::path(pathStr);
@@ -106,7 +114,7 @@ void wrapUtils()
     def("stripInstanceIndexFromUfePath", _stripInstanceIndexFromUfePath, (arg("ufePathString")));
     def("ufePathToPrim", _ufePathToPrim);
     def("ufePathToInstanceIndex", _ufePathToInstanceIndex);
-    def("isEditTargetLayerModifiable", UsdUfe::isEditTargetLayerModifiable);
+    def("isEditTargetLayerModifiable", _isEditTargetLayerModifiable);
     def("getTime", _getTime);
     def("isAttributeEditAllowed", _isAttributeEditAllowed);
 }
diff --git a/test/lib/ufe/testContextOps.py b/test/lib/ufe/testContextOps.py
index b983970ba9..dc7a660a66 100644
--- a/test/lib/ufe/testContextOps.py
+++ b/test/lib/ufe/testContextOps.py
@@ -919,13 +919,15 @@ def createMaterial(proxyShape):
         assert ufe.Hierarchy.createItem(ufe.PathString.path(expectedPath))
 
         # Case 6: A non-scope object named "mtl" exists and a scope named "mtl2" exists.
-        # The new material should get created in a new scope named "mtl1".
+        # The new material should get created in a new scope named "mtl3".
+        # This follows normal Maya naming standard where it increments the largest numerical
+        # suffix (even if there are gaps).
         proxyShape = createProxyShape()
         proxyShapePath = ufe.PathString.string(proxyShape.path())
         addNewPrim(proxyShape, "Def", materialsScopeName)
         addNewPrim(proxyShape, "Scope", materialsScopeName + "2")
         createMaterial(proxyShape)
-        expectedPath = proxyShapePath + ",/" + materialsScopeName + "1/" + materialName
+        expectedPath = proxyShapePath + ",/" + materialsScopeName + "3/" + materialName
         assert ufe.Hierarchy.createItem(ufe.PathString.path(expectedPath))
 
         # Case 7: A non-scope object named "mtl" exists and a scope named "mtlBingBong" exists.
@@ -948,8 +950,11 @@ def createMaterial(proxyShape):
         for scopeNamePostfix in scopeNamePostfixes:
             addNewPrim(proxyShape, "Scope", materialsScopeName + scopeNamePostfix)
 
+        # Again here follow the normal Maya naming standard which increments the largest
+        # numerical suffix (1337).
         createMaterial(proxyShape)
-        expectedPath = proxyShapePath + ",/" + materialsScopeName + "1/" + materialName
+        expectedPath = proxyShapePath + ",/" + materialsScopeName + "1338/" + materialName
+        print(expectedPath)
         assert ufe.Hierarchy.createItem(ufe.PathString.path(expectedPath))
 
         # Case 9: Multiple non-scope object named "mtl", "mtl1", ..., "mtl3" exists and multiple 
@@ -967,7 +972,7 @@ def createMaterial(proxyShape):
             addNewPrim(proxyShape, "Scope", materialsScopeName + scopeNamePostfix)
 
         createMaterial(proxyShape)
-        expectedPath = proxyShapePath + ",/" + materialsScopeName + "4/" + materialName
+        expectedPath = proxyShapePath + ",/" + materialsScopeName + "1338/" + materialName
         assert ufe.Hierarchy.createItem(ufe.PathString.path(expectedPath))
 
         # Case 10: Multiple non-scope object named "mtl", "mtl1", ..., "mtl3" exists and multiple