diff --git a/src/h1_htx.c b/src/h1_htx.c
index 734f9cbce..30e2b229e 100644
--- a/src/h1_htx.c
+++ b/src/h1_htx.c
@@ -278,7 +278,7 @@ static int h1_postparse_res_hdrs(struct h1m *h1m, union h1_sl *h1sl, struct htx
 		return 0;
 	}
 
-	if (((h1m->flags & H1_MF_METH_CONNECT) && code == 200) || code == 101) {
+	if (((h1m->flags & H1_MF_METH_CONNECT) && code >= 200 && code < 300) || code == 101) {
 		/* Switch successful replies to CONNECT requests and
 		 * protocol switching to tunnel mode. */
 		h1_set_tunnel_mode(h1m);
diff --git a/src/http_ana.c b/src/http_ana.c
index 5dfd41bde..db98a5469 100644
--- a/src/http_ana.c
+++ b/src/http_ana.c
@@ -1635,7 +1635,7 @@ int http_wait_for_response(struct stream *s, struct channel *rep, int an_bit)
 		http_capture_headers(htx, s->res_cap, sess->fe->rsp_cap);
 
 	/* Skip parsing if no content length is possible. */
-	if (unlikely((txn->meth == HTTP_METH_CONNECT && txn->status == 200) ||
+	if (unlikely((txn->meth == HTTP_METH_CONNECT && txn->status >= 200 && txn->status < 300) ||
 		     txn->status == 101)) {
 		/* Either we've established an explicit tunnel, or we're
 		 * switching the protocol. In both cases, we're very unlikely
@@ -2132,7 +2132,7 @@ int http_response_forward_body(struct stream *s, struct channel *res, int an_bit
 	if (msg->msg_state >= HTTP_MSG_ENDING)
 		goto ending;
 
-	if ((txn->meth == HTTP_METH_CONNECT && txn->status == 200) || txn->status == 101 ||
+	if ((txn->meth == HTTP_METH_CONNECT && txn->status >= 200 && txn->status < 300) || txn->status == 101 ||
 	    (!(msg->flags & HTTP_MSGF_XFER_LEN) && !HAS_RSP_DATA_FILTERS(s))) {
 		msg->msg_state = HTTP_MSG_ENDING;
 		goto ending;
@@ -2187,7 +2187,7 @@ int http_response_forward_body(struct stream *s, struct channel *res, int an_bit
 		}
 	}
 
-	if ((txn->meth == HTTP_METH_CONNECT && txn->status == 200) || txn->status == 101 ||
+	if ((txn->meth == HTTP_METH_CONNECT && txn->status >= 200 && txn->status < 300) || txn->status == 101 ||
 	    !(msg->flags & HTTP_MSGF_XFER_LEN)) {
 		msg->msg_state = HTTP_MSG_TUNNEL;
 		goto ending;
diff --git a/src/mux_h1.c b/src/mux_h1.c
index f50b9d844..2bb532810 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -934,7 +934,7 @@ static void h1_set_cli_conn_mode(struct h1s *h1s, struct h1m *h1m)
 
 	if (h1m->flags & H1_MF_RESP) {
 		/* Output direction: second pass */
-		if ((h1s->meth == HTTP_METH_CONNECT && h1s->status == 200) ||
+		if ((h1s->meth == HTTP_METH_CONNECT && h1s->status >= 200 && h1s->status < 300) ||
 		    h1s->status == 101) {
 			/* Either we've established an explicit tunnel, or we're
 			 * switching the protocol. In both cases, we're very unlikely to
@@ -994,7 +994,7 @@ static void h1_set_srv_conn_mode(struct h1s *h1s, struct h1m *h1m)
 
 	if (h1m->flags & H1_MF_RESP) {
 		/* Input direction: second pass */
-		if ((h1s->meth == HTTP_METH_CONNECT && h1s->status == 200) ||
+		if ((h1s->meth == HTTP_METH_CONNECT && h1s->status >= 200 && h1s->status < 300) ||
 		    h1s->status == 101) {
 			/* Either we've established an explicit tunnel, or we're
 			 * switching the protocol. In both cases, we're very unlikely to
@@ -1817,8 +1817,8 @@ static size_t h1_process_output(struct h1c *h1c, struct buffer *buf, size_t coun
 				if ((h1s->meth != HTTP_METH_CONNECT &&
 				     (h1m->flags & (H1_MF_VER_11|H1_MF_RESP|H1_MF_CLEN|H1_MF_CHNK|H1_MF_XFER_LEN)) ==
 				     (H1_MF_VER_11|H1_MF_XFER_LEN)) ||
-				    (h1s->status >= 200 && h1s->status != 204 && h1s->status != 304 &&
-				     h1s->meth != HTTP_METH_HEAD && !(h1s->meth == HTTP_METH_CONNECT && h1s->status == 200) &&
+				    (h1s->status >= 200 && h1s->status != 204 && h1s->status != 304 && h1s->meth != HTTP_METH_HEAD &&
+				     !(h1s->meth == HTTP_METH_CONNECT && h1s->status >= 200 && h1s->status < 300) &&
 				     (h1m->flags & (H1_MF_VER_11|H1_MF_RESP|H1_MF_CLEN|H1_MF_CHNK|H1_MF_XFER_LEN)) ==
 				     (H1_MF_VER_11|H1_MF_RESP|H1_MF_XFER_LEN))) {
 					/* chunking needed but header not seen */
@@ -1862,7 +1862,7 @@ static size_t h1_process_output(struct h1c *h1c, struct buffer *buf, size_t coun
 					h1_set_req_tunnel_mode(h1s);
 				}
 				else if ((h1m->flags & H1_MF_RESP) &&
-					 ((h1s->meth == HTTP_METH_CONNECT && h1s->status == 200) || h1s->status == 101)) {
+					 ((h1s->meth == HTTP_METH_CONNECT && h1s->status >= 200 && h1s->status < 300) || h1s->status == 101)) {
 					/* a successful reply to a CONNECT or a protocol switching is sent
 					 * to the client. Switch the response to tunnel mode.
 					 */