diff --git a/src/h1_htx.c b/src/h1_htx.c
index 70e4b2cb0..6ea19d265 100644
--- a/src/h1_htx.c
+++ b/src/h1_htx.c
@@ -178,7 +178,18 @@ static int h1_postparse_req_hdrs(struct h1m *h1m, union h1_sl *h1sl, struct htx
 		h1m->curr_len = h1m->body_len = 0;
 	}
 
+
 	flags = h1m_htx_sl_flags(h1m);
+	if ((flags & (HTX_SL_F_CONN_UPG|HTX_SL_F_BODYLESS)) == HTX_SL_F_CONN_UPG) {
+		int i;
+
+		for (i = 0; hdrs[i].n.len; i++) {
+			if (isteqi(hdrs[i].n, ist("upgrade")))
+				hdrs[i].v = IST_NULL;
+		}
+		h1m->flags &=~ H1_MF_CONN_UPG;
+		flags &= ~HTX_SL_F_CONN_UPG;
+	}
 	sl = htx_add_stline(htx, HTX_BLK_REQ_SL, flags, meth, uri, vsn);
 	if (!sl || !htx_add_all_headers(htx, hdrs))
 		goto error;
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 5fd492a11..45506c65d 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -5288,7 +5288,7 @@ static size_t h2s_bck_make_req_headers(struct h2s *h2s, struct htx *htx)
 				continue;
 
 			/* Convert connection: upgrade to Extended connect from rfc 8441 */
-			if (isteqi(list[hdr].n, ist("connection"))) {
+			if ((sl->flags & HTX_SL_F_CONN_UPG) && isteqi(list[hdr].n, ist("connection"))) {
 				/* rfc 7230 #6.1 Connection = list of tokens */
 				struct ist connection_ist = list[hdr].v;
 				do {
@@ -5306,7 +5306,7 @@ static size_t h2s_bck_make_req_headers(struct h2s *h2s, struct htx *htx)
 				} while (istlen(connection_ist));
 			}
 
-			if (isteq(list[hdr].n, ist("upgrade"))) {
+			if ((sl->flags & HTX_SL_F_CONN_UPG) && isteq(list[hdr].n, ist("upgrade"))) {
 				/* rfc 7230 #6.7 Upgrade = list of protocols
 				 * rfc 8441 #4 Extended connect = :protocol is single-valued
 				 *