diff --git a/src/h1_htx.c b/src/h1_htx.c
index dc6accabb..5ef995f7d 100644
--- a/src/h1_htx.c
+++ b/src/h1_htx.c
@@ -296,10 +296,6 @@ static int h1_postparse_res_hdrs(struct h1m *h1m, union h1_sl *h1sl, struct htx
 		/* Responses with a known body length. */
 		h1m->flags |= H1_MF_XFER_LEN;
 	}
-	else {
-		/* Responses with an unknown body length */
-		h1m->state = H1_MSG_TUNNEL;
-	}
 
 	used = htx_used_space(htx);
 	flags = h1m_htx_sl_flags(h1m);
diff --git a/src/mux_fcgi.c b/src/mux_fcgi.c
index 765cff3b8..65e511b65 100644
--- a/src/mux_fcgi.c
+++ b/src/mux_fcgi.c
@@ -3374,6 +3374,16 @@ static size_t fcgi_strm_parse_response(struct fcgi_strm *fstrm, struct buffer *b
 		else if (h1m->state < H1_MSG_TRAILERS) {
 			TRACE_PROTO("parsing response payload", FCGI_EV_RSP_DATA|FCGI_EV_RSP_BODY, fconn->conn, fstrm);
 			ret = fcgi_strm_parse_data(fstrm, h1m, &htx, &fstrm->rxbuf, &total, count, buf);
+
+			if (!(h1m->flags & H1_MF_XFER_LEN) && fstrm->state != FCGI_SS_ERROR &&
+			    (fstrm->flags & FCGI_SF_ES_RCVD) && b_data(&fstrm->rxbuf) == total) {
+				TRACE_DEVEL("end of data", FCGI_EV_RSP_DATA, fconn->conn, fstrm);
+				if (!(h1m->flags & H1_MF_VER_11))
+					fstrm->flags |= FCGI_SF_H1_PARSING_DONE;
+				h1m->state = H1_MSG_DONE;
+				TRACE_USER("H1 response fully rcvd", FCGI_EV_RSP_DATA|FCGI_EV_RSP_EOM, fconn->conn, fstrm, htx);
+			}
+
 			if (!ret && h1m->state != H1_MSG_DONE)
 				break;
 
@@ -3402,23 +3412,6 @@ static size_t fcgi_strm_parse_response(struct fcgi_strm *fstrm, struct buffer *b
 			}
 			break;
 		}
-		else if (h1m->state == H1_MSG_TUNNEL) {
-			TRACE_PROTO("parsing response tunneled data", FCGI_EV_RSP_DATA, fconn->conn, fstrm);
-			ret = fcgi_strm_parse_data(fstrm, h1m, &htx, &fstrm->rxbuf, &total, count, buf);
-
-			if (fstrm->state != FCGI_SS_ERROR &&
-			    (fstrm->flags & FCGI_SF_ES_RCVD) && b_data(&fstrm->rxbuf) == total) {
-				TRACE_DEVEL("end of tunneled data", FCGI_EV_RSP_DATA, fconn->conn, fstrm);
-				if ((h1m->flags & (H1_MF_VER_11|H1_MF_XFER_LEN)) != H1_MF_VER_11)
-					fstrm->flags |= FCGI_SF_H1_PARSING_DONE;
-				h1m->state = H1_MSG_DONE;
-				TRACE_USER("H1 response fully rcvd", FCGI_EV_RSP_DATA|FCGI_EV_RSP_EOM, fconn->conn, fstrm, htx);
-			}
-			if (!ret && h1m->state != H1_MSG_DONE)
-				break;
-
-			TRACE_PROTO("rcvd H1 response tunneled data", FCGI_EV_RSP_DATA, fconn->conn, fstrm, htx);
-		}
 		else {
 			htx->flags |= HTX_FL_PROCESSING_ERROR;
 			TRACE_PROTO("processing error", FCGI_EV_RSP_DATA, fconn->conn, fstrm);
diff --git a/src/mux_h1.c b/src/mux_h1.c
index 19f8240f4..00bb6dc51 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -1651,8 +1651,9 @@ static size_t h1_process_input(struct h1c *h1c, struct buffer *buf, size_t count
 		h1s->cs->flags &= ~(CS_FL_RCV_MORE | CS_FL_WANT_ROOM);
 		if (h1s->flags & H1S_F_REOS) {
 			h1s->cs->flags |= CS_FL_EOS;
-			if (h1m->state >= H1_MSG_DONE) {
-				/* DONE or TUNNEL, set EOI on the conn-stream */
+			if (h1m->state >= H1_MSG_DONE || !(h1m->flags & H1_MF_XFER_LEN)) {
+				/* DONE or TUNNEL or SHUTR without XFER_LEN, set
+				 * EOI on the conn-stream */
 				h1s->cs->flags |= CS_FL_EOI;
 			}
 			else if (h1m->state > H1_MSG_LAST_LF && h1m->state < H1_MSG_DONE)