diff --git a/docs/run/authorization.md b/docs/run/authorization.md
index fefd0ed34a..7a7a5dd2fd 100644
--- a/docs/run/authorization.md
+++ b/docs/run/authorization.md
@@ -67,17 +67,28 @@ You registered one tool. The second route is the SDK's.
 This document is how a client that has never heard of your server finds its way in: it reads `authorization_servers` and goes there for a token. You wrote none of it.
 
 !!! check
-    Call `/mcp` with no token (or with one your verifier returned `None` for) and the request is
+    Call `/mcp` with no token and the request is
     stopped at the door:
 
     ```text
     HTTP/1.1 401 Unauthorized
-    WWW-Authenticate: Bearer error="invalid_token", error_description="Authentication required", resource_metadata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp"
+    WWW-Authenticate: Bearer resour…ata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp", scope="notes:read"
+    ```
+
+    Nothing was parsed and no tool ran. The challenge carries no error code, because no
+    credentials were presented (RFC 6750 Section 3.1), and it names the `scope` a token needs.
+
+    A token your verifier returned `None` for is a different case: a credential *was* presented
+    and was rejected, so it is answered with the error code.
+
+    ```text
+    HTTP/1.1 401 Unauthorized
+    WWW-Authenticate: Bearer error="invalid_token", error_description="Authentication required", resource_metadata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp", scope="notes:read"
 
     {"error": "invalid_token", "error_description": "Authentication required"}
     ```
 
-    Nothing was parsed and no tool ran. And that `resource_metadata` pointer in `WWW-Authenticate` is
+    And that `resource_metadata` pointer in `WWW-Authenticate` is
     what makes discovery automatic: 401 -> metadata document -> authorization server -> token -> retry.
 
 !!! warning
diff --git a/src/mcp/server/auth/middleware/bearer_auth.py b/src/mcp/server/auth/middleware/bearer_auth.py
index 1a070cd29d..0e76e80fd1 100644
--- a/src/mcp/server/auth/middleware/bearer_auth.py
+++ b/src/mcp/server/auth/middleware/bearer_auth.py
@@ -5,6 +5,7 @@
 
 from pydantic import AnyHttpUrl, ValidationError
 from starlette.authentication import AuthCredentials, AuthenticationBackend, SimpleUser
+from starlette.datastructures import Headers
 from starlette.requests import HTTPConnection
 from starlette.types import Receive, Scope, Send
 
@@ -115,8 +116,17 @@ def __init__(
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         auth_user = scope.get("user")
         if not isinstance(auth_user, AuthenticatedUser):
+            # RFC 6750 3.1: a request with no credentials SHOULD NOT include an
+            # error code. Only a presented-but-invalid token gets
+            # error="invalid_token". Advertise the required scopes either way.
+            headers = Headers(scope=scope)
+            presented = headers.get("authorization") is not None
             await self._send_auth_error(
-                send, status_code=401, error="invalid_token", description="Authentication required"
+                send,
+                status_code=401,
+                error="invalid_token" if presented else None,
+                description="Authentication required" if presented else None,
+                scope=self.required_scopes or None,
             )
             return
 
@@ -126,24 +136,44 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
             # auth_credentials should always be provided; this is just paranoia
             if auth_credentials is None or required_scope not in auth_credentials.scopes:
                 await self._send_auth_error(
-                    send, status_code=403, error="insufficient_scope", description=f"Required scope: {required_scope}"
+                    send,
+                    status_code=403,
+                    error="insufficient_scope",
+                    description=f"Required scope: {required_scope}",
+                    scope=[required_scope],
                 )
                 return
 
         await self.app(scope, receive, send)
 
-    async def _send_auth_error(self, send: Send, status_code: int, error: str, description: str) -> None:
+    async def _send_auth_error(
+        self,
+        send: Send,
+        status_code: int,
+        error: str | None = None,
+        description: str | None = None,
+        scope: list[str] | None = None,
+    ) -> None:
         """Send an authentication error response with WWW-Authenticate header."""
         # Build WWW-Authenticate header value
-        www_auth_parts = [f'error="{error}"', f'error_description="{description}"']
+        www_auth_parts = []
+        if error:
+            www_auth_parts.append(f'error="{error}"')
+        if description:
+            www_auth_parts.append(f'error_description="{description}"')
         if self.resource_metadata_url:
             www_auth_parts.append(f'resource_metadata="{self.resource_metadata_url}"')
+        if scope:
+            # Join outside the f-string: nested same-type quotes in an f-string
+            # need PEP 701 (Python 3.12+), and this project supports 3.11.
+            scope_value = " ".join(scope)
+            www_auth_parts.append(f'scope="{scope_value}"')
 
         www_authenticate = f"Bearer {', '.join(www_auth_parts)}"
 
         # Send response
-        body = {"error": error, "error_description": description}
-        body_bytes = json.dumps(body).encode()
+        body = {} if error is None else {"error": error, "error_description": description}
+        body_bytes = json.dumps(body).encode() if body else b""
 
         await send(
             {
diff --git a/tests/docs_src/test_authorization.py b/tests/docs_src/test_authorization.py
index 00c9adc81c..832c98d018 100644
--- a/tests/docs_src/test_authorization.py
+++ b/tests/docs_src/test_authorization.py
@@ -60,15 +60,20 @@ async def test_a_request_without_a_token_never_reaches_the_protocol() -> None:
     async with httpx2.AsyncClient(transport=transport, base_url="http://127.0.0.1:8000") as http_client:
         response = await http_client.post("/mcp", json={})
     assert response.status_code == 401
-    assert response.json() == {"error": "invalid_token", "error_description": "Authentication required"}
+    # No credentials were presented, so RFC 6750 Section 3.1 says the challenge
+    # carries no error code and the body is empty; the required scope is advertised.
+    assert response.content == b""
     assert response.headers["www-authenticate"] == (
-        'Bearer error="invalid_token", error_description="Authentication required", '
-        'resource_metadata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp"'
+        'Bearer resource_metadata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp", scope="notes:read"'
     )
 
 
 async def test_a_token_the_verifier_rejects_gets_the_same_401() -> None:
-    """tutorial001: `verify_token` returning `None` and a missing header are indistinguishable to the caller."""
+    """tutorial001: a rejected token is answered 401 `invalid_token`.
+
+    A credential WAS presented, so RFC 6750 Section 3.1 keeps the error code; the challenge
+    additionally advertises the required scope.
+    """
     transport = httpx2.ASGITransport(app=tutorial001.mcp.streamable_http_app())
     async with httpx2.AsyncClient(transport=transport, base_url="http://127.0.0.1:8000") as http_client:
         response = await http_client.post("/mcp", json={}, headers={"Authorization": "Bearer not-a-real-token"})
diff --git a/tests/interaction/_requirements.py b/tests/interaction/_requirements.py
index 1d9033b307..807b1ec907 100644
--- a/tests/interaction/_requirements.py
+++ b/tests/interaction/_requirements.py
@@ -2871,9 +2871,6 @@ def __post_init__(self) -> None:
         behavior="A malformed bearer token or token-verification failure returns 401 with WWW-Authenticate.",
         transports=("streamable-http",),
         note="Auth is enforced at the HTTP layer; 401 is an HTTP status code.",
-        divergence=Divergence(
-            note="The challenge carries no `scope` parameter; see the note on hosting:auth:missing-401.",
-        ),
     ),
     "hosting:auth:metadata-endpoints": Requirement(
         source=f"{SPEC_BASE_URL}/basic/authorization#authorization-server-location",
@@ -2893,15 +2890,6 @@ def __post_init__(self) -> None:
         ),
         transports=("streamable-http",),
         note="Auth is enforced at the HTTP layer; 401 is an HTTP status code.",
-        divergence=Divergence(
-            note=(
-                "The SDK never emits a `scope` parameter in any WWW-Authenticate challenge — neither the "
-                "discovery-time 401 (#protected-resource-metadata-discovery-requirements SHOULD) nor the "
-                "runtime 403 (#runtime-insufficient-scope-errors SHOULD); and for the no-credentials case "
-                'it emits error="invalid_token", which RFC 6750 Section 3.1 says SHOULD NOT appear when no '
-                "authentication information was presented."
-            ),
-        ),
     ),
     "hosting:auth:prm:authorization-servers-field": Requirement(
         source=f"{SPEC_BASE_URL}/basic/authorization#authorization-server-location",
@@ -2928,13 +2916,6 @@ def __post_init__(self) -> None:
         ),
         transports=("streamable-http",),
         note="Auth is enforced at the HTTP layer; 403 is an HTTP status code.",
-        divergence=Divergence(
-            note=(
-                'The SDK emits error="insufficient_scope" and error_description but never the `scope` '
-                "parameter the spec SHOULD include; the SDK client reads `scope` from this header to drive "
-                "step-up (utils.py extract_scope_from_www_auth) — a resource-server/client asymmetry."
-            ),
-        ),
     ),
     "hosting:auth:as:authorize-requires-pkce": Requirement(
         source=f"{SPEC_BASE_URL}/basic/authorization#authorization-code-protection",
diff --git a/tests/interaction/auth/test_bearer.py b/tests/interaction/auth/test_bearer.py
index aa42c50dfb..e0d65df488 100644
--- a/tests/interaction/auth/test_bearer.py
+++ b/tests/interaction/auth/test_bearer.py
@@ -87,36 +87,33 @@ def parse_www_authenticate(value: str) -> dict[str, str]:
 async def test_a_request_with_no_authorization_header_is_challenged_with_resource_metadata(
     protected: httpx2.AsyncClient,
 ) -> None:
-    """No `Authorization` header → 401 with a `WWW-Authenticate` carrying `resource_metadata`.
-
-    The snapshot pins current behaviour: the SDK collapses the no-header, unknown-token, and
-    expired-token cases into one challenge (`error="invalid_token"`, no `scope` parameter). The
-    spec says the discovery-time challenge SHOULD include `scope` and RFC 6750 says the
-    no-credentials case SHOULD NOT carry an error code; both gaps are recorded as the divergence
-    on this requirement. Asserting the dict equals an exact key set also pins that no parameter
-    appears twice.
+    """No `Authorization` header → 401 with a `WWW-Authenticate` carrying `resource_metadata` and `scope`.
+
+    RFC 6750 Section 3.1 says a request that carried no credentials SHOULD NOT be answered with an
+    error code, and the spec's discovery-time requirement says the challenge SHOULD advertise the
+    required `scope`. Both hold here: the challenge carries `resource_metadata` and `scope` and no
+    `error`/`error_description`, and the body is empty. Asserting the dict equals an exact key set
+    also pins that no parameter appears twice.
     """
     response = await post_mcp(protected)
 
     assert response.status_code == 401
     assert response.headers["www-authenticate"] == snapshot(
-        'Bearer error="invalid_token", error_description="Authentication required", '
-        'resource_metadata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp"'
+        'Bearer resource_metadata="http://127.0.0.1:8000/.well-known/oauth-protected-resource/mcp", scope="mcp:read"'
     )
     assert parse_www_authenticate(response.headers["www-authenticate"]) == {
-        "error": "invalid_token",
-        "error_description": "Authentication required",
         "resource_metadata": RESOURCE_METADATA_URL,
+        "scope": REQUIRED_SCOPE,
     }
-    assert response.json() == snapshot({"error": "invalid_token", "error_description": "Authentication required"})
+    assert response.content == b""
 
 
 @requirement("hosting:auth:invalid-401")
 async def test_an_unrecognized_bearer_token_is_answered_401_invalid_token(protected: httpx2.AsyncClient) -> None:
     """A token the verifier does not recognize is answered 401 `invalid_token`.
 
-    The challenge is identical to the no-header case (the backend returns `None` for both); the
-    missing `scope` parameter is the recorded divergence on this requirement.
+    A credential WAS presented, so RFC 6750 Section 3.1 keeps the `invalid_token` error code; the
+    challenge also advertises the required `scope`.
     """
     response = await post_mcp(protected, bearer="tok-unknown")
 
@@ -125,6 +122,7 @@ async def test_an_unrecognized_bearer_token_is_answered_401_invalid_token(protec
         "error": "invalid_token",
         "error_description": "Authentication required",
         "resource_metadata": RESOURCE_METADATA_URL,
+        "scope": REQUIRED_SCOPE,
     }
 
 
@@ -143,15 +141,15 @@ async def test_an_expired_token_is_answered_401(protected: httpx2.AsyncClient) -
 
 
 @requirement("hosting:auth:scope-403")
-async def test_a_token_missing_a_required_scope_is_answered_403_insufficient_scope_without_a_scope_param(
+async def test_a_token_missing_a_required_scope_is_answered_403_insufficient_scope(
     protected: httpx2.AsyncClient,
 ) -> None:
-    """A token lacking the required scope is answered 403 `insufficient_scope`, with no `scope` parameter.
+    """A token lacking the required scope is answered 403 `insufficient_scope`, naming the scope.
 
     The spec's runtime-insufficient-scope guidance says the challenge SHOULD include `scope`
-    naming the required scope; the SDK never emits it, recorded as the divergence on this
-    requirement. The SDK client reads `scope` from this header to drive step-up, so the gap is
-    a resource-server/client asymmetry.
+    naming the required scope, and the SDK client reads `scope` from this header to drive
+    step-up (utils.py extract_scope_from_www_auth) — a resource-server/client asymmetry the
+    SDK now closes.
     """
     response = await post_mcp(protected, bearer="tok-noscope")
 
@@ -161,8 +159,8 @@ async def test_a_token_missing_a_required_scope_is_answered_403_insufficient_sco
         "error": "insufficient_scope",
         "error_description": f"Required scope: {REQUIRED_SCOPE}",
         "resource_metadata": RESOURCE_METADATA_URL,
+        "scope": REQUIRED_SCOPE,
     }
-    assert "scope" not in parsed
 
 
 @requirement("hosting:auth:aud-validation")
@@ -214,4 +212,9 @@ async def test_an_access_token_in_the_query_string_is_not_accepted(protected: ht
     response = await post_mcp(protected, query={"access_token": "tok-valid"})
 
     assert response.status_code == 401
-    assert parse_www_authenticate(response.headers["www-authenticate"])["error"] == "invalid_token"
+    # No credentials were presented (the query string is never consulted), so the
+    # challenge carries no error code at all (RFC 6750 Section 3.1) and advertises
+    # the required scope instead.
+    parsed = parse_www_authenticate(response.headers["www-authenticate"])
+    assert "error" not in parsed
+    assert parsed["scope"] == REQUIRED_SCOPE