diff --git a/doc/configuration.txt b/doc/configuration.txt
index 809adebf9..27e370230 100644
--- a/doc/configuration.txt
+++ b/doc/configuration.txt
@@ -9826,7 +9826,9 @@ timeout client-fin <timeout>
   FIN_WAIT state for too long when clients do not disconnect cleanly. This
   problem is particularly common long connections such as RDP or WebSocket.
   Note that this timeout can override "timeout tunnel" when a connection shuts
-  down in one direction.
+  down in one direction. It is applied to idle HTTP/2 connections once a GOAWAY
+  frame was sent, often indicating an expectation that the connection quickly
+  ends.
 
   This parameter is specific to frontends, but can be specified once for all in
   "defaults" sections. By default it is not set, so half-closed connections
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 13d1bb316..90bd36e63 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -104,6 +104,7 @@ struct h2c {
 	int32_t mfs; /* mux's max frame size */
 
 	int timeout;        /* idle timeout duration in ticks */
+	int shut_timeout;   /* idle timeout duration in ticks after GOAWAY was sent */
 	struct task *task;  /* timeout management task */
 	struct eb_root streams_by_id; /* all active streams by their ID */
 	struct list send_list; /* list of blocked streams requesting to send */
@@ -332,7 +333,10 @@ static int h2c_frt_init(struct connection *conn)
 		goto fail;
 
 
-	h2c->timeout = sess->fe->timeout.client;
+	h2c->shut_timeout = h2c->timeout = sess->fe->timeout.client;
+	if (tick_isset(sess->fe->timeout.clientfin))
+		h2c->shut_timeout = sess->fe->timeout.clientfin;
+
 	h2c->task = NULL;
 	if (tick_isset(h2c->timeout)) {
 		t = task_new(tid_bit);
@@ -2143,7 +2147,7 @@ static int h2_wake(struct connection *conn)
 
 	if (h2c->task) {
 		if (eb_is_empty(&h2c->streams_by_id)) {
-			h2c->task->expire = tick_add(now_ms, h2c->timeout);
+			h2c->task->expire = tick_add(now_ms, h2c->last_sid < 0 ? h2c->timeout : h2c->shut_timeout);
 			task_queue(h2c->task);
 		}
 		else
@@ -2175,6 +2179,7 @@ static struct task *h2_timeout_task(struct task *t)
 	}
 
 	/* try to send but no need to insist */
+	h2c->last_sid = h2c->max_id;
 	if (h2c_send_goaway_error(h2c, NULL) <= 0)
 		h2c->flags |= H2_CF_GOAWAY_FAILED;
 
@@ -2310,7 +2315,7 @@ static void h2_detach(struct conn_stream *cs)
 		}
 		else if (h2c->task) {
 			if (eb_is_empty(&h2c->streams_by_id)) {
-				h2c->task->expire = tick_add(now_ms, h2c->timeout);
+				h2c->task->expire = tick_add(now_ms, h2c->last_sid < 0 ? h2c->timeout : h2c->shut_timeout);
 				task_queue(h2c->task);
 			}
 			else