diff --git a/internal/rproxy/limits_test.go b/internal/rproxy/limits_test.go
index 685f05b..3f99abb 100644
--- a/internal/rproxy/limits_test.go
+++ b/internal/rproxy/limits_test.go
@@ -12,6 +12,7 @@ import (
 	"os"
 	"strconv"
 	"strings"
+	"sync"
 	"sync/atomic"
 	"testing"
 	"time"
@@ -807,8 +808,10 @@ func TestAVisitorThatStopsSendingAfterTheAppHasAnsweredGetsTheAnswer(t *testing.
 	app := startApp(t, func(w http.ResponseWriter, _ *http.Request) {
 		_, _ = io.WriteString(w, greeting)
 	})
+	// The request time limit is far longer than dial's deadline, so that a busy
+	// host cannot use it up before the app's answer arrives.
 	addr, _ := startRProxy(t, standIn.URL, app.URL, map[string]string{
-		maxRequestTime: "3000",
+		maxRequestTime: "120000",
 	})
 
 	// Far more announced than sent, so that Go's server answers for the app
@@ -869,11 +872,11 @@ func TestAVisitorThatStopsALittleShortGetsTheAppsAnswerAtOnce(t *testing.T) {
 
 	standIn := startWAF(t, allow)
 	app := startApp(t, answerBeforeTheBody)
-	// The request time limit is longer than the 10 seconds the status and headers
-	// of an answer have to be sent, and than dial's deadline.
+	// Both time limits are far longer than dial's deadline, so that the answer
+	// has to come before either runs out, and a busy host cannot use them up.
 	addr, _ := startRProxy(t, standIn.URL, app.URL, map[string]string{
-		maxRequestTime:  "15000",
-		maxResponseTime: "300",
+		maxRequestTime:  "120000",
+		maxResponseTime: "60000",
 	})
 
 	conn := dial(t, addr)
@@ -910,6 +913,62 @@ func TestAVisitorThatStopsALittleShortIsReadUntilTheRequestTimeLimit(t *testing.
 	}
 }
 
+func TestAVisitorThatStopsALittleShortHasTheConnectionClosedWhenTheAnswerIsCutOff(
+	t *testing.T,
+) {
+	t.Parallel()
+
+	const limit = 300 * time.Millisecond
+
+	headersRead := make(chan struct{})
+	// letAppSendBody also runs when the test ends, as the app's server waits for
+	// the app.
+	letAppSendBody := sync.OnceFunc(func() { close(headersRead) })
+	standIn := startWAF(t, allow)
+	// The app sends its body once the visitor has the status and headers and the
+	// response time limit has run out since, so that rproxy cannot send it.
+	app := startApp(t, func(w http.ResponseWriter, r *http.Request) {
+		rc := http.NewResponseController(w)
+		_ = rc.EnableFullDuplex()
+
+		w.Header().Set(contentLengthHeader, strconv.Itoa(len(greeting)))
+		_ = rc.Flush()
+
+		<-headersRead
+		time.Sleep(limit)
+
+		_, _ = io.WriteString(w, greeting)
+		_ = rc.Flush()
+		_, _ = io.Copy(io.Discard, r.Body)
+	})
+
+	t.Cleanup(letAppSendBody)
+
+	// The request time limit is far longer than dial's deadline.
+	addr, _ := startRProxy(t, standIn.URL, app.URL, map[string]string{
+		maxRequestTime:  "120000",
+		maxResponseTime: strconv.FormatInt(limit.Milliseconds(), 10),
+	})
+
+	conn := dial(t, addr)
+	sendAllButALittle(t, conn)
+
+	res, err := http.ReadResponse(bufio.NewReader(conn), nil)
+	if err != nil {
+		t.Fatalf("read the answer: %v", err)
+	}
+
+	letAppSendBody()
+
+	// If the connection stays open, dial's deadline ends this read with a timeout.
+	body, err := io.ReadAll(res.Body)
+	_ = res.Body.Close()
+
+	if len(body) != 0 || !errors.Is(err, io.ErrUnexpectedEOF) {
+		t.Errorf("read %q (%v), want the connection closed", body, err)
+	}
+}
+
 func TestAVisitorThatStopsSendingWhileTheAppWorksGetsNoAnswer(t *testing.T) {
 	t.Parallel()