diff --git a/internal/rproxy/request.go b/internal/rproxy/request.go
index 170b14e..bee4367 100644
--- a/internal/rproxy/request.go
+++ b/internal/rproxy/request.go
@@ -272,6 +272,10 @@ func (rq *request) modifyResponse(res *http.Response) error {
 
 	rq.closeAfterAnswer()
 
+	// An answer that arrives before the app has been sent the whole request ends
+	// the request, and SWRP_MAX_RESPONSE_TIME_MS starts.
+	rq.startResponseTimer(requestEnd)
+
 	res.Body = &responseBody{body: limitBody(res.Body, maxBytes), rq: rq}
 	rq.out.afterStatus = rq.setResponseDeadline
 
@@ -386,14 +390,17 @@ func (rq *request) finish(ctx context.Context) {
 
 	// After a cut-off answer, the reading of a body that has not arrived whole
 	// ends now. Go's server would otherwise keep the connection open while it
-	// reads the rest. A flush fails if the time to send the answer ran out, and
+	// reads the rest. The app's answer is cut off by a refusal once it is passed
+	// on, as afterStatus shows, since a refusal ends the request to the app. Any
+	// answer is cut off when the time to send it runs out: a flush then fails, and
 	// every flush after a failed one fails too. ReverseProxy ignores the failure,
 	// but panics if it was still waiting for more of the app's answer; finish runs
 	// either way. Before a status, a flush would send a 200; after a 101,
 	// ReverseProxy has taken over the connection.
 	switch {
-	case rq.out.status != 0 && rq.out.status != http.StatusSwitchingProtocols &&
-		errors.Is(rq.rc.Flush(), os.ErrDeadlineExceeded):
+	case rq.out.afterStatus != nil && rq.refused.Load() != 0,
+		rq.out.status != 0 && rq.out.status != http.StatusSwitchingProtocols &&
+			errors.Is(rq.rc.Flush(), os.ErrDeadlineExceeded):
 		rq.stopPassingOnBody(time.Now())
 	case rq.refused.Load() == 0:
 		rq.stopPassingOnBody(rq.requestDeadline())
@@ -553,19 +560,29 @@ func (rq *request) wroteRequest(info httptrace.WroteRequestInfo) {
 	requestEnd := rq.endRequest()
 
 	rq.mu.Lock()
-	defer rq.mu.Unlock()
+	stopTimer(rq.requestTimer)
+	rq.mu.Unlock()
 
-	if rq.timersStopped {
+	rq.startResponseTimer(requestEnd)
+}
+
+// startResponseTimer starts SWRP_MAX_RESPONSE_TIME_MS, which runs from
+// requestEnd, unless it has started already.
+func (rq *request) startResponseTimer(requestEnd time.Time) {
+	limit := rq.h.config.MaxResponseTime
+	if limit == 0 {
 		return
 	}
 
-	stopTimer(rq.requestTimer)
+	rq.mu.Lock()
+	defer rq.mu.Unlock()
 
-	limit := rq.h.config.MaxResponseTime
-	if limit > 0 {
-		rq.responseTimer = time.AfterFunc(time.Until(requestEnd.Add(limit)),
-			rq.responseTimedOut)
+	if rq.timersStopped || rq.responseTimer != nil {
+		return
 	}
+
+	rq.responseTimer = time.AfterFunc(time.Until(requestEnd.Add(limit)),
+		rq.responseTimedOut)
 }
 
 // responseTimedOut is called when SWRP_MAX_RESPONSE_TIME_MS runs out before the