diff --git a/CHANGELOG.md b/CHANGELOG.md
index be4ac902..b75b6580 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -82,7 +82,7 @@ All notable changes to `mcp/sdk` will be documented in this file.
 * Fix a client request that timed out (elicitation, sampling) staying in the session's pending requests: `Protocol::checkResponse()` now expires it, answering with the `Request timed out` error, so the transports no longer implement the timeout themselves.
 * Fix a handshake-era Streamable HTTP stream pinning its PHP worker until the elicitation (or other client request) times out after the client disconnected: the idle stream now sends a keep-alive comment and stops once the connection is aborted.
 * [BC Break] Fix concurrent stdio tool calls that report progress, log, elicit or sample never finishing: `StdioTransport` keeps every suspended fiber and resumes each with the answer to its own request. A transport passes the suspended `\Fiber` as last argument to the pending-requests provider and the fiber yield handler.
-* Add an opt-in per-session lock, `Builder::setSessionLock()`, serializing the concurrent requests of one session so none of them overwrites what another saved: pending server requests, client answers, client info. `FileSessionLock` locks with `flock()` next to `FileSessionStore`, `SymfonyLockSessionLock` uses a symfony/lock store for sessions shared across machines; `SessionLockInterface` takes custom ones. Off by default. A request that cannot get the lock in time is answered with `503` and a JSON-RPC error; a failing lock backend with `503` and `The session lock is unavailable.`. `SessionLockTimeoutException`, a `SessionLockException`, tells a timeout from a backend failure. `SymfonyLockSessionLock` releases its locks from a shutdown function after a fatal error in a handler.
+* Add an opt-in per-session lock, `Builder::setSessionLock()`, serializing the concurrent requests of one session so none of them overwrites what another saved: pending server requests, client answers, client info. `FileSessionLock` locks with `flock()` next to `FileSessionStore`, `SymfonyLockSessionLock` uses a symfony/lock store for sessions shared across machines; `SessionLockInterface` takes custom ones. Off by default. A request that cannot get the lock in time is answered with `503` and a JSON-RPC error; a failing lock backend with `503` and `Session lock is unavailable.`, like a failing session store. `SessionLockTimeoutException`, a `SessionLockException`, tells a timeout from a backend failure. `SymfonyLockSessionLock` releases its locks from a shutdown function after a fatal error in a handler.
 * `Protocol::__construct()` takes an optional `SessionLockInterface $sessionLock` as its last argument.
 * `FileSessionStore::gc()` also removes the lock files of expired sessions a `FileSessionLock` in the same directory left behind, each only while no request holds it.
 * Resume a suspended handler with an error when the transport fails to store what it sends to the client next, instead of resuming it with `null`; `ClientGateway::notify()` then throws a `ClientException`.
diff --git a/docs/run/sessions.md b/docs/run/sessions.md
index 2b8a5327..0803af49 100644
--- a/docs/run/sessions.md
+++ b/docs/run/sessions.md
@@ -177,7 +177,7 @@ one after the other.
 A request that cannot get the lock within the timeout (30 seconds by default, the constructors' `$timeout`)
 is answered with HTTP `503` and a JSON-RPC error, instead of running on a session another request is about
 to overwrite. A lock backend that fails, e.g. a Redis that refuses connections, is answered with `503` too,
-but at once, with the error message `The session lock is unavailable.`, and logged as an error with its cause;
+but at once, with the error message `Session lock is unavailable.`, and logged as an error with its cause;
 a timeout is only logged as a warning. A handler that resumed after the client answered gets an error when the lock cannot be had to
 store its next request or notification: the `ClientGateway` method throws a `ClientException`, and the
 message does not reach the client.
diff --git a/src/Server/Protocol.php b/src/Server/Protocol.php
index 7c8a7be0..1d89caca 100644
--- a/src/Server/Protocol.php
+++ b/src/Server/Protocol.php
@@ -78,7 +78,6 @@ class Protocol
 
     /** Answer to a request that could not get its session's lock in time, see {@see SessionLockInterface}. */
     private const SESSION_BUSY_MESSAGE = 'Another request of this session is still being processed.';
-    private const SESSION_LOCK_UNAVAILABLE_MESSAGE = 'The session lock is unavailable.';
 
     /**
      * Seconds past its timeout after which a pending client request counts as abandoned by its stream.
@@ -257,13 +256,13 @@ private function doProcessInput(TransportInterface $transport, string $input, ?U
 
         if ($takesLock) {
             try {
-                $refusal = $this->acquireSessionLock($sessionId) ? null : self::SESSION_BUSY_MESSAGE;
+                $refusal = $this->acquireSessionLock($sessionId) ? null : Error::forServerError(self::SESSION_BUSY_MESSAGE, self::findResponseId($input));
             } catch (SessionLockException) {
-                $refusal = self::SESSION_LOCK_UNAVAILABLE_MESSAGE;
+                $refusal = Error::forInternalError('Session lock is unavailable.', self::findResponseId($input));
             }
 
             if (null !== $refusal) {
-                $this->sendResponse($transport, Error::forServerError($refusal, self::findResponseId($input)), null, ['status_code' => 503]);
+                $this->sendResponse($transport, $refusal, null, ['status_code' => 503]);
 
                 return;
             }
diff --git a/tests/Unit/Server/ProtocolSessionLockTest.php b/tests/Unit/Server/ProtocolSessionLockTest.php
index 039fca4d..b3dbf8a3 100644
--- a/tests/Unit/Server/ProtocolSessionLockTest.php
+++ b/tests/Unit/Server/ProtocolSessionLockTest.php
@@ -197,8 +197,8 @@ public function testUnavailableLockIsRefusedAndLoggedWithItsCause(): void
 
         $error = json_decode($transport->sent[0]['message'], true);
         $this->assertSame(1, $error['id']);
-        $this->assertSame(Error::SERVER_ERROR, $error['error']['code']);
-        $this->assertSame('The session lock is unavailable.', $error['error']['message']);
+        $this->assertSame(Error::INTERNAL_ERROR, $error['error']['code']);
+        $this->assertSame('Session lock is unavailable.', $error['error']['message']);
 
         $errors = $logger->messagesAt(LogLevel::ERROR);
         $this->assertCount(1, $errors);