diff --git a/test/cli/backup.test.ts b/test/cli/backup.test.ts
index 7330b72..1938a4b 100644
--- a/test/cli/backup.test.ts
+++ b/test/cli/backup.test.ts
@@ -909,6 +909,27 @@ describe("the backup lock", () => {
         expect(existsSync(lockPath(outDir))).toBe(false);
         await lib.close();
     });
+
+    // `runBackup` takes a library object from its caller. With a
+    // `contentConcurrency` below 1, or one that is not a number, it would
+    // back up no original and report no error. It rejects any that is not a
+    // positive integer, as `BoundedPool` does, before it takes the lock,
+    // which would create the download directory, and before it asks the
+    // library for anything: the object here has nothing else.
+    it("rejects a library whose contentConcurrency is not a positive integer, before taking the lock", async () => {
+        const outDir = join(root, "backup");
+        for (const contentConcurrency of [undefined, 0, -1, 1.5, NaN]) {
+            const lib = { contentConcurrency } as unknown as BackupLibrary;
+
+            await expect(
+                runBackup(lib, { downloadDirectory: outDir }),
+            ).rejects.toThrow(
+                `contentConcurrency must be a positive integer, got ${contentConcurrency}`,
+            );
+
+            expect(existsSync(outDir)).toBe(false);
+        }
+    });
 });
 
 // Also serves ML data: file 100 has `ML_PAYLOAD`, the other two have none.