diff --git a/bin/varnishd/http1/cache_http1_pipe.c b/bin/varnishd/http1/cache_http1_pipe.c
index c55f688031f..af7a70de0d7 100644
--- a/bin/varnishd/http1/cache_http1_pipe.c
+++ b/bin/varnishd/http1/cache_http1_pipe.c
@@ -40,6 +40,7 @@
 
 #include "cache_http1.h"
 #include "vtcp.h"
+#include "vtim.h"
 
 #include "VSC_vbe.h"
 
@@ -117,7 +118,8 @@ stream_close_t
 V1P_Process(const struct req *req, int fd, struct v1p_acct *v1a)
 {
 	struct pollfd fds[2];
-	vtim_dur tmo;
+	vtim_dur tmo, tmo_task;
+	vtim_real deadline;
 	stream_close_t sc;
 	int i, j;
 
@@ -141,6 +143,10 @@ V1P_Process(const struct req *req, int fd, struct v1p_acct *v1a)
 	fds[1].fd = req->sp->fd;
 	fds[1].events = POLLIN;
 
+	deadline = cache_param->deadline_pipe;
+	if (deadline > 0.)
+		deadline += req->sp->t_idle;
+
 	sc = SC_TX_PIPE;
 	while (fds[0].fd > -1 || fds[1].fd > -1) {
 		fds[0].revents = 0;
@@ -148,6 +154,11 @@ V1P_Process(const struct req *req, int fd, struct v1p_acct *v1a)
 		tmo = cache_param->pipe_timeout;
 		if (tmo == 0.)
 			tmo = -1.;
+		if (deadline > 0.) {
+			tmo_task = deadline - VTIM_real();
+			tmo = (tmo > 0.) ? vmin(tmo, tmo_task) : tmo_task;
+			tmo = vmax(tmo, 0.);
+		}
 		i = poll(fds, 2, (int)(tmo * 1e3));
 		if (i == 0)
 			sc = SC_RX_TIMEOUT;
diff --git a/bin/varnishtest/tests/s00013.vtc b/bin/varnishtest/tests/s00013.vtc
index 06e89871bf1..e7dd04aee8a 100644
--- a/bin/varnishtest/tests/s00013.vtc
+++ b/bin/varnishtest/tests/s00013.vtc
@@ -10,13 +10,31 @@ server s1 {
 	rxreq
 	txresp -hdr "transfer-encoding: chunked"
 	expect_close
+
+	accept
+	rxreq
+	txresp -hdr "transfer-encoding: chunked"
+	expect_close
+
+	accept
+	non_fatal
+	rxreq
+	txresp -hdr "transfer-encoding: chunked"
+	loop 20 {
+		chunkedlen 1
+		delay 0.1
+	}
 } -start
 
 varnish v1 -cliok "param.set pipe_timeout 0s"
+varnish v1 -cliok "param.set deadline_pipe 0s"
 varnish v1 -vcl+backend "" -start
 
-logexpect l1 -v v1 -q "Timestamp:PipeSess[2] > 1.0" {
-	expect 1001 * ReqMethod PIPE
+logexpect l1 -v v1 -g raw -q SessClose {
+	expect 1000 * SessClose {^TX_PIPE 1\.}
+	expect 1003 * SessClose {^RX_TIMEOUT 0\.}
+	expect 1006 * SessClose {^RX_TIMEOUT 1\.}
+	expect 1009 * SessClose {^RX_TIMEOUT 1\.}
 } -start
 
 client c1 {
@@ -25,11 +43,20 @@ client c1 {
 	rxresp
 } -run
 
-logexpect l1 -wait
+varnish v1 -cliok "param.set pipe_timeout 500ms"
+varnish v1 -cliok "param.set deadline_pipe 0s"
+client c1 -run
+
+varnish v1 -cliok "param.set pipe_timeout 0s"
+varnish v1 -cliok "param.set deadline_pipe 1.1s"
+client c1 -run
 
 varnish v1 -cliok "param.set pipe_timeout 500ms"
+varnish v1 -cliok "param.set deadline_pipe 1.1s"
 client c1 -run
 
-varnish v1 -expect MAIN.s_pipe == 2
+logexpect l1 -wait
+
+varnish v1 -expect MAIN.s_pipe == 4
 varnish v1 -expect MAIN.sc_tx_pipe == 1
-varnish v1 -expect MAIN.sc_rx_timeout == 1
+varnish v1 -expect MAIN.sc_rx_timeout == 3