diff --git a/src/content-type-repair.test.ts b/src/content-type-repair.test.ts
index 98819f3..bf9bf89 100644
--- a/src/content-type-repair.test.ts
+++ b/src/content-type-repair.test.ts
@@ -79,6 +79,16 @@ describe("Codex content-type repair — missing content-type on 2xx SSE response
     expect(response.headers.get("content-type")).toBe("text/event-stream");
   });
 
+  test("repairs a relative URL instead of throwing", async () => {
+    const repaired = withCodexContentTypeRepair(
+      fetchReturning(new Response("data: {}\n\n", { status: 200 })),
+    );
+    const response = await repaired(`/backend-api${CODEX_RESPONSES_PATH}`, {
+      headers: { accept: "text/event-stream" },
+    });
+    expect(response.headers.get("content-type")).toBe("text/event-stream");
+  });
+
   test("treats an empty content-type as missing", async () => {
     const repaired = withCodexContentTypeRepair(
       fetchReturning(
diff --git a/src/content-type-repair.ts b/src/content-type-repair.ts
index 96d9247..46cb5b5 100644
--- a/src/content-type-repair.ts
+++ b/src/content-type-repair.ts
@@ -54,8 +54,8 @@ function acceptedContentType(
 export function withCodexContentTypeRepair(fetchImpl: FetchLike): FetchLike {
   return async (input, init) => {
     const response = await fetchImpl(input, init);
-    if (!new URL(requestURL(input)).pathname.endsWith(CODEX_RESPONSES_PATH))
-      return response;
+    const { pathname } = new URL(requestURL(input), "http://localhost");
+    if (!pathname.endsWith(CODEX_RESPONSES_PATH)) return response;
     if (!response.ok) return response;
     if (response.headers.get("content-type")) return response;
     const declared = acceptedContentType(input, init);