diff --git a/masque/shapes/path.py b/masque/shapes/path.py
index d4c7b24..706e2f4 100644
--- a/masque/shapes/path.py
+++ b/masque/shapes/path.py
@@ -265,6 +265,14 @@ class Path(Shape):
             if self.cap_extensions is None:
                 return True
             return tuple(self.cap_extensions) < tuple(other.cap_extensions)
+        if not numpy.array_equal(self.vertices, other.vertices):
+            min_len = min(self.vertices.shape[0], other.vertices.shape[0])
+            eq_mask = self.vertices[:min_len] != other.vertices[:min_len]
+            eq_lt = self.vertices[:min_len] < other.vertices[:min_len]
+            eq_lt_masked = eq_lt[eq_mask]
+            if eq_lt_masked.size > 0:
+                return eq_lt_masked.flat[0]
+            return self.vertices.shape[0] < other.vertices.shape[0]
         if self.repetition != other.repetition:
             return rep2key(self.repetition) < rep2key(other.repetition)
         return annotations_lt(self.annotations, other.annotations)