diff --git a/app/__init__.py b/app/__init__.py
index c9e346d..384fb20 100644
--- a/app/__init__.py
+++ b/app/__init__.py
@@ -181,6 +181,15 @@ def setup_error_handlers(app: Flask) -> None:
             mimetype="application/json",
         )
 
+    @app.errorhandler(405)
+    def method_not_allowed(error: HTTPException) -> Response:
+        """Handle 405 Method Not Allowed errors."""
+        return Response(
+            json.dumps({"error": "Method not allowed"}),
+            status=405,
+            mimetype="application/json",
+        )
+
     @app.errorhandler(500)
     def internal_error(error: HTTPException) -> Response:
         """Handle 500 Internal Server errors."""
@@ -199,6 +208,9 @@ def setup_error_handlers(app: Flask) -> None:
     @app.errorhandler(Exception)
     def handle_exception(error: Exception) -> Response:
         """Handle unhandled exceptions with generic 500 response."""
+        # Re-raise HTTP exceptions to their proper handlers
+        if isinstance(error, HTTPException):
+            return error  # type: ignore[return-value]
         app.logger.exception(
             "Unhandled exception: %s [rid=%s]", str(error), getattr(g, "request_id", "-")
         )