diff --git a/include/haproxy/stream_interface.h b/include/haproxy/stream_interface.h
index 9492e8279..a1f67c2dc 100644
--- a/include/haproxy/stream_interface.h
+++ b/include/haproxy/stream_interface.h
@@ -242,6 +242,15 @@ static inline int si_rx_blocked(const struct stream_interface *si)
 	return !!(si->flags & SI_FL_RXBLK_ANY);
 }
 
+
+/* Returns non-zero if the stream interface's Rx path is blocked because of lack
+ * of room in the input buffer.
+ */
+static inline int si_rx_blocked_room(const struct stream_interface *si)
+{
+	return !!(si->flags & SI_FL_RXBLK_ROOM);
+}
+
 /* Returns non-zero if the stream interface's endpoint is ready to receive */
 static inline int si_rx_endp_ready(const struct stream_interface *si)
 {
diff --git a/src/http_ana.c b/src/http_ana.c
index 3480e9620..7d9abdbbc 100644
--- a/src/http_ana.c
+++ b/src/http_ana.c
@@ -4060,8 +4060,10 @@ enum rule_result http_wait_for_msg_body(struct stream *s, struct channel *chn,
 	/* Now we're in HTTP_MSG_DATA. We just need to know if all data have
 	 * been received or if the buffer is full.
 	 */
-	if ((htx->flags & HTX_FL_EOM) || htx_get_tail_type(htx) > HTX_BLK_DATA ||
-	    channel_htx_full(chn, htx, global.tune.maxrewrite))
+	if ((htx->flags & HTX_FL_EOM) ||
+	    htx_get_tail_type(htx) > HTX_BLK_DATA ||
+	    channel_htx_full(chn, htx, global.tune.maxrewrite) ||
+	    si_rx_blocked_room(chn_prod(chn)))
 		goto end;
 
 	if (bytes) {
diff --git a/src/tcp_rules.c b/src/tcp_rules.c
index bbd5820b4..72b1cd37c 100644
--- a/src/tcp_rules.c
+++ b/src/tcp_rules.c
@@ -113,6 +113,7 @@ int tcp_inspect_request(struct stream *s, struct channel *req, int an_bit)
 	 */
 
 	if ((req->flags & CF_SHUTR) || channel_full(req, global.tune.maxrewrite) ||
+	    si_rx_blocked_room(chn_prod(req)) ||
 	    !s->be->tcp_req.inspect_delay || tick_is_expired(s->rules_exp, now_ms))
 		partial = SMP_OPT_FINAL;
 	else
@@ -268,6 +269,7 @@ int tcp_inspect_response(struct stream *s, struct channel *rep, int an_bit)
 	 * - if one rule returns KO, then return KO
 	 */
 	if ((rep->flags & CF_SHUTR) || channel_full(rep, global.tune.maxrewrite) ||
+	    si_rx_blocked_room(chn_prod(rep)) ||
 	    !s->be->tcp_rep.inspect_delay || tick_is_expired(s->rules_exp, now_ms))
 		partial = SMP_OPT_FINAL;
 	else