diff --git a/lib/redact-patterns.ts b/lib/redact-patterns.ts
index 858ade4f2..7007d49ef 100644
--- a/lib/redact-patterns.ts
+++ b/lib/redact-patterns.ts
@@ -392,6 +392,28 @@ export function isDotenvFilename(match: RegExpExecArray): boolean {
   return spanStart > 0 && input[spanStart - 1] === ".";
 }
 
+/** Extensions that mark a `<name>.local.<ext>` span as a file. Closed on
+ * purpose: `.md` is also Moldova's TLD, but no internal suffix sits in front
+ * of a public one, so after `.local` it can only be an extension. */
+const LOCAL_CONFIG_EXTENSIONS = /^\.(?:md|json|jsonc|ya?ml|toml|ini|conf|txt)\b/i;
+
+/**
+ * True when an `internal.hostname` span is the stem of a per-machine config
+ * FILENAME (`CLAUDE.local.md`, `settings.local.json`, `values.staging.yaml`)
+ * rather than a host (#2962). The pattern's `\b` stops at the dot before the
+ * extension, so `CLAUDE.local.md` reported `CLAUDE.local`. Claude Code's own
+ * per-user files are named this way, so any decision or doc that mentions
+ * them failed closed in the non-interactive stores.
+ *
+ * Exempts ONLY a span immediately followed by `.<known extension>` and a word
+ * boundary. `printer.local.` at the end of a sentence still reports, and so
+ * do `printer.local`, `printer.local/md` and `printer.local.mdx`.
+ */
+export function isLocalConfigFilename(match: RegExpExecArray): boolean {
+  const { end } = spanBounds(match);
+  return LOCAL_CONFIG_EXTENSIONS.test((match.input ?? "").slice(end, end + 8));
+}
+
 /**
  * True when the matched span sits ENTIRELY inside a UUID.
  *
@@ -894,8 +916,9 @@ export const PATTERNS: RedactPattern[] = [
     category: "internal",
     description: "Internal hostname (*.internal/.corp/.local/.prod/.staging)",
     regex: /\b([a-z0-9][a-z0-9\-]*\.(?:internal|corp|local|lan|prod|staging))\b/i,
-    // `.env.local` and friends are filenames, not hosts. See isDotenvFilename.
-    validate: (_span, match) => !isDotenvFilename(match),
+    // `.env.local`, `CLAUDE.local.md` and friends are filenames, not hosts.
+    // See isDotenvFilename and isLocalConfigFilename.
+    validate: (_span, match) => !isDotenvFilename(match) && !isLocalConfigFilename(match),
   },
   {
     id: "internal.url_private",
diff --git a/test/redact-context-exemptions.test.ts b/test/redact-context-exemptions.test.ts
index b4b3b588e..895d259f3 100644
--- a/test/redact-context-exemptions.test.ts
+++ b/test/redact-context-exemptions.test.ts
@@ -105,3 +105,28 @@ describe("env.kv: a function call assigned to a credential name is code (#2899)"
     ],
   );
 });
+
+describe("internal.hostname: per-machine config filenames are not hosts (#2962, #2740)", () => {
+  table(
+    "internal.hostname",
+    "MEDIUM",
+    [
+      "Edit CLAUDE.local.md and settings.local.json",
+      "no `CLAUDE.local.md`, no @import",
+      "edit .claude/settings.local.json",
+      "helm -f values.staging.yaml",
+      "config.prod.toml is read first",
+      "npm run dev -- --env-file=.env.local",
+      "copy .env.local to .env.staging",
+    ],
+    [
+      "ssh build.local",
+      "ping printer.local.",
+      "http://printer.local/md",
+      "printer.local.mdx is odd",
+      "curl http://settings.local:8080/health",
+      "the api.corp gateway",
+      "connect to build-7.internal",
+    ],
+  );
+});