diff --git a/federationapi/routing/backfill.go b/federationapi/routing/backfill.go
index 31005209f..82f6cbabf 100644
--- a/federationapi/routing/backfill.go
+++ b/federationapi/routing/backfill.go
@@ -51,6 +51,12 @@ func Backfill(
 		}
 	}
 
+	// If we don't think we belong to this room then don't waste the effort
+	// responding to expensive requests for it.
+	if err := ErrorIfLocalServerNotInRoom(httpReq.Context(), rsAPI, roomID); err != nil {
+		return *err
+	}
+
 	// Check if all of the required parameters are there.
 	eIDs, exists = httpReq.URL.Query()["v"]
 	if !exists {
diff --git a/federationapi/routing/eventauth.go b/federationapi/routing/eventauth.go
index 0a03a0cb4..e83cb8ad2 100644
--- a/federationapi/routing/eventauth.go
+++ b/federationapi/routing/eventauth.go
@@ -30,6 +30,12 @@ func GetEventAuth(
 	roomID string,
 	eventID string,
 ) util.JSONResponse {
+	// If we don't think we belong to this room then don't waste the effort
+	// responding to expensive requests for it.
+	if err := ErrorIfLocalServerNotInRoom(ctx, rsAPI, roomID); err != nil {
+		return *err
+	}
+
 	event, resErr := fetchEvent(ctx, rsAPI, eventID)
 	if resErr != nil {
 		return *resErr
diff --git a/federationapi/routing/missingevents.go b/federationapi/routing/missingevents.go
index dd3df7aa9..b826d69c4 100644
--- a/federationapi/routing/missingevents.go
+++ b/federationapi/routing/missingevents.go
@@ -45,6 +45,12 @@ func GetMissingEvents(
 		}
 	}
 
+	// If we don't think we belong to this room then don't waste the effort
+	// responding to expensive requests for it.
+	if err := ErrorIfLocalServerNotInRoom(httpReq.Context(), rsAPI, roomID); err != nil {
+		return *err
+	}
+
 	var eventsResponse api.QueryMissingEventsResponse
 	if err := rsAPI.QueryMissingEvents(
 		httpReq.Context(), &api.QueryMissingEventsRequest{
diff --git a/federationapi/routing/routing.go b/federationapi/routing/routing.go
index a085ed780..6d24c8b40 100644
--- a/federationapi/routing/routing.go
+++ b/federationapi/routing/routing.go
@@ -15,6 +15,8 @@
 package routing
 
 import (
+	"context"
+	"fmt"
 	"net/http"
 
 	"github.com/gorilla/mux"
@@ -24,6 +26,7 @@ import (
 	"github.com/matrix-org/dendrite/internal"
 	"github.com/matrix-org/dendrite/internal/httputil"
 	keyserverAPI "github.com/matrix-org/dendrite/keyserver/api"
+	"github.com/matrix-org/dendrite/roomserver/api"
 	roomserverAPI "github.com/matrix-org/dendrite/roomserver/api"
 	"github.com/matrix-org/dendrite/setup/config"
 	userapi "github.com/matrix-org/dendrite/userapi/api"
@@ -491,3 +494,27 @@ func Setup(
 		}),
 	).Methods(http.MethodGet)
 }
+
+func ErrorIfLocalServerNotInRoom(
+	ctx context.Context,
+	rsAPI api.RoomserverInternalAPI,
+	roomID string,
+) *util.JSONResponse {
+	// Check if we think we're in this room. If we aren't then
+	// we won't waste CPU cycles serving this request.
+	joinedReq := &api.QueryServerJoinedToRoomRequest{
+		RoomID: roomID,
+	}
+	joinedRes := &api.QueryServerJoinedToRoomResponse{}
+	if err := rsAPI.QueryServerJoinedToRoom(ctx, joinedReq, joinedRes); err != nil {
+		res := util.ErrorResponse(err)
+		return &res
+	}
+	if !joinedRes.IsInRoom {
+		return &util.JSONResponse{
+			Code: http.StatusNotFound,
+			JSON: jsonerror.NotFound(fmt.Sprintf("This server is not joined to room %s", roomID)),
+		}
+	}
+	return nil
+}
diff --git a/federationapi/routing/state.go b/federationapi/routing/state.go
index a202c92c2..e2b67776a 100644
--- a/federationapi/routing/state.go
+++ b/federationapi/routing/state.go
@@ -101,6 +101,12 @@ func getState(
 	roomID string,
 	eventID string,
 ) (stateEvents, authEvents []*gomatrixserverlib.HeaderedEvent, errRes *util.JSONResponse) {
+	// If we don't think we belong to this room then don't waste the effort
+	// responding to expensive requests for it.
+	if err := ErrorIfLocalServerNotInRoom(ctx, rsAPI, roomID); err != nil {
+		return nil, nil, err
+	}
+
 	event, resErr := fetchEvent(ctx, rsAPI, eventID)
 	if resErr != nil {
 		return nil, nil, resErr