diff --git a/internal/proxy/request.go b/internal/proxy/request.go
index 5eedc12..1155ea2 100644
--- a/internal/proxy/request.go
+++ b/internal/proxy/request.go
@@ -715,6 +715,12 @@ func (rq *request) requestTimedOut(limit string) {
 			action: requestlog.ActionTimedOut,
 			limit:  limit,
 		})
+		// Go's server, before it sends the app's answer, and the
+		// transport, as it closes the body, read what is left of a body
+		// under 256 KiB without requestBody.Read, so waiting is false
+		// while they wait for the client. Those reads end when the client
+		// is out of time.
+		rq.stopReadingBody(rq.clientRequestDeadline())
 
 		return
 	}
diff --git a/internal/proxy/timeouts_test.go b/internal/proxy/timeouts_test.go
index ff00c8c..8018d1b 100644
--- a/internal/proxy/timeouts_test.go
+++ b/internal/proxy/timeouts_test.go
@@ -7,6 +7,7 @@ import (
 	"net/http"
 	"net/http/httptest"
 	"strconv"
+	"strings"
 	"sync"
 	"sync/atomic"
 	"testing"
@@ -248,6 +249,59 @@ func TestClientStopsSendingAfterTheAppHasAnswered(t *testing.T) {
 	wantLimitHits(t, addr, clientRequestTimeout, 1)
 }
 
+func TestClientStopsSendingWithLittleOfItsBodyLeft(t *testing.T) {
+	t.Parallel()
+
+	// appClosed is closed once smallwebwaf has closed its connection to
+	// the app, which it does once it has the app's answer.
+	appClosed := make(chan struct{})
+
+	// The app answers as soon as it has the headers, without reading the
+	// body, and says it closes the connection.
+	app := startApp(t, func(w http.ResponseWriter, _ *http.Request) {
+		conn, buf, err := http.NewResponseController(w).Hijack()
+		if err != nil {
+			return
+		}
+
+		_, _ = buf.WriteString("HTTP/1.1 404 Not Found\r\n" +
+			"Content-Length: 0\r\nConnection: close\r\n\r\n")
+		_ = buf.Flush()
+		_, _ = io.Copy(io.Discard, buf.Reader)
+		_ = conn.Close()
+
+		close(appClosed)
+	})
+	addr, out := startProxy(t, app.URL, map[string]string{
+		clientRequestTimeout: shortTimeoutSetting,
+		metricsToken:         token,
+	})
+
+	// Less than 256 KiB of the body is left after the first bytes, little
+	// enough for Go's server in smallwebwaf to read the rest itself before
+	// it sends the app's answer.
+	start := time.Now()
+	conn := dial(t, addr)
+	send(t, conn, "POST /upload HTTP/1.1\r\nHost: app\r\nContent-Length: 200000\r\n\r\n"+
+		"the first bytes")
+
+	select {
+	case <-appClosed:
+	case <-time.After(waitLimit):
+		t.Fatal("smallwebwaf did not close its connection to the app")
+	}
+
+	// More of the body, which can no longer go to the app, and then
+	// nothing.
+	send(t, conn, strings.Repeat("x", 8<<10))
+
+	got := readResponse(t, conn)
+	wantTimedOut(t, start)
+	wantStatus(t, got, http.StatusNotFound)
+	wantLine(t, out.requestLine(t), http.StatusNotFound, requestlog.ActionTimedOut)
+	wantLimitHits(t, addr, clientRequestTimeout, 1)
+}
+
 func TestAppTooSlowToAnswer(t *testing.T) {
 	t.Parallel()