diff --git a/lambdas/api/handler.py b/lambdas/api/handler.py
index 56b4ca0..a467f62 100644
--- a/lambdas/api/handler.py
+++ b/lambdas/api/handler.py
@@ -87,8 +87,9 @@ def _base_url(event: dict) -> str | None:
     # A custom domain (base-path mapping) serves the stage at the root, so the
     # public URL has NO /{stage} segment; only the raw execute-api host carries
     # it. Emitting /{stage} for a custom-domain request would advertise a
-    # broken server URL in the docs.
-    if ".execute-api." in domain:
+    # broken server URL in the docs. All API Gateway default domains end with
+    # .amazonaws.com, so check the suffix rather than a substring.
+    if domain.endswith(".amazonaws.com"):
         return f"https://{domain}/{stage}" if stage else None
     return f"https://{domain}"