diff --git a/src/mux_h1.c b/src/mux_h1.c
index eff0a5e..5c66660 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -62,17 +62,18 @@
 #define H1C_F_UPG_H2C        0x00080000 /* set if an upgrade to h2 should be done */
 #define H1C_F_CO_MSG_MORE    0x00100000 /* set if CO_SFL_MSG_MORE must be set when calling xprt->snd_buf() */
 #define H1C_F_CO_STREAMER    0x00200000 /* set if CO_SFL_STREAMER must be set when calling xprt->snd_buf() */
-#define H1C_F_RX_BLK         0x00400000 /* Don't process more input data, waiting sync with output side */
-#define H1C_F_TX_BLK         0x00800000 /* Don't process more output data, waiting sync with input side */
 
-/* 0x01000000 - 0x40000000 unusued*/
+/* 0x00400000 - 0x40000000 unusued*/
 #define H1C_F_IS_BACK        0x80000000 /* Set on outgoing connection */
 
 /*
  * H1 Stream flags (32 bits)
  */
 #define H1S_F_NONE           0x00000000
-/* 0x00000001..0x00000004 unused */
+
+#define H1S_F_RX_BLK         0x00100000 /* Don't process more input data, waiting sync with output side */
+#define H1S_F_TX_BLK         0x00200000 /* Don't process more output data, waiting sync with input side */
+/* 0x00000004 unused */
 #define H1S_F_REOS           0x00000008 /* End of input stream seen even if not delivered yet */
 #define H1S_F_WANT_KAL       0x00000010
 #define H1S_F_WANT_TUN       0x00000020
@@ -697,6 +698,7 @@
 	if (!h1s)
 		goto fail;
 
+	h1s->flags |= H1S_F_RX_BLK;
 	h1s->cs = cs;
 	h1s->sess = sess;
 	cs->ctx = h1s;
@@ -727,7 +729,7 @@
 
 		h1_release_buf(h1c, &h1s->rxbuf);
 
-		h1c->flags &= ~(H1C_F_TX_BLK|H1C_F_RX_BLK|H1C_F_WANT_SPLICE|
+		h1c->flags &= ~(H1C_F_WANT_SPLICE|
 				H1C_F_ST_EMBRYONIC|H1C_F_ST_ATTACHED|H1C_F_ST_READY|
 				H1C_F_OUT_FULL|H1C_F_OUT_ALLOC|H1C_F_IN_SALLOC|
 				H1C_F_CO_MSG_MORE|H1C_F_CO_STREAMER);
@@ -793,7 +795,7 @@
 	h1c->idle_exp = TICK_ETERNITY;
 
 	if (conn_is_back(conn)) {
-		h1c->flags |= (H1C_F_IS_BACK|H1C_F_RX_BLK);
+		h1c->flags |= H1C_F_IS_BACK;
 		h1c->shut_timeout = h1c->timeout = proxy->timeout.server;
 		if (tick_isset(proxy->timeout.serverfin))
 			h1c->shut_timeout = proxy->timeout.serverfin;
@@ -1284,15 +1286,15 @@
 
 	TRACE_STATE("switch H1 stream in tunnel mode", H1_EV_TX_DATA|H1_EV_TX_HDRS, h1c->conn, h1s);
 
-	if (h1c->flags & H1C_F_RX_BLK) {
-		h1c->flags &= ~H1C_F_RX_BLK;
+	if (h1s->flags & H1S_F_RX_BLK) {
+		h1s->flags &= ~H1S_F_RX_BLK;
 		h1_wake_stream_for_recv(h1s);
-		TRACE_STATE("Re-enable input processing on h1c", H1_EV_RX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+		TRACE_STATE("Re-enable input processing", H1_EV_RX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 	}
-	if (h1c->flags & H1C_F_TX_BLK) {
-		h1c->flags &= ~H1C_F_TX_BLK;
+	if (h1s->flags & H1S_F_TX_BLK) {
+		h1s->flags &= ~H1S_F_TX_BLK;
 		h1_wake_stream_for_send(h1s);
-		TRACE_STATE("Re-enable output processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+		TRACE_STATE("Re-enable output processing", H1_EV_TX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 	}
 }
 
@@ -1518,7 +1520,7 @@
 	if (h1s->flags & (H1S_F_PARSING_ERROR|H1S_F_NOT_IMPL_ERROR))
 		goto end;
 
-	if (h1c->flags & H1C_F_RX_BLK)
+	if (h1s->flags & H1S_F_RX_BLK)
 		goto out;
 
 	do {
@@ -1576,13 +1578,13 @@
 			else {
 				if (h1s->req.state < H1_MSG_DONE || h1s->res.state < H1_MSG_DONE) {
 					/* Unfinished transaction: block this input side waiting the end of the output side */
-					h1c->flags |= H1C_F_RX_BLK;
-					TRACE_STATE("Disable input processing on h1c", H1_EV_RX_DATA|H1_EV_H1C_BLK, h1c->conn, h1s);
+					h1s->flags |= H1S_F_RX_BLK;
+					TRACE_STATE("Disable input processing", H1_EV_RX_DATA|H1_EV_H1S_BLK, h1c->conn, h1s);
 				}
-				if (h1c->flags & H1C_F_TX_BLK) {
-					h1c->flags &= ~H1C_F_TX_BLK;
+				if (h1s->flags & H1S_F_TX_BLK) {
+					h1s->flags &= ~H1S_F_TX_BLK;
 					h1_wake_stream_for_send(h1s);
-					TRACE_STATE("Re-enable output processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+					TRACE_STATE("Re-enable output processing", H1_EV_TX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 				}
 				break;
 			}
@@ -1602,7 +1604,7 @@
 		}
 
 		count -= htx_used_space(htx) - used;
-	} while (!(h1s->flags & (H1S_F_PARSING_ERROR|H1S_F_NOT_IMPL_ERROR)) && !(h1c->flags & H1C_F_RX_BLK));
+	} while (!(h1s->flags & (H1S_F_PARSING_ERROR|H1S_F_NOT_IMPL_ERROR|H1S_F_RX_BLK)));
 
 
 	if (h1s->flags & (H1S_F_PARSING_ERROR|H1S_F_NOT_IMPL_ERROR)) {
@@ -1696,10 +1698,10 @@
 				TRACE_ERROR("message aborted, set error on CS", H1_EV_RX_DATA|H1_EV_H1S_ERR, h1c->conn, h1s);
 			}
 
-			if (h1c->flags & H1C_F_TX_BLK) {
-				h1c->flags &= ~H1C_F_TX_BLK;
+			if (h1s->flags & H1S_F_TX_BLK) {
+				h1s->flags &= ~H1S_F_TX_BLK;
 				h1_wake_stream_for_send(h1s);
-				TRACE_STATE("Re-enable output processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+				TRACE_STATE("Re-enable output processing", H1_EV_TX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 			}
 		}
 	}
@@ -1739,10 +1741,7 @@
 	if (htx_is_empty(chn_htx))
 		goto end;
 
-	if (h1s->flags & H1S_F_PROCESSING_ERROR)
-		goto end;
-
-	if (h1c->flags & H1C_F_TX_BLK)
+	if (h1s->flags & (H1S_F_PROCESSING_ERROR|H1S_F_TX_BLK))
 		goto end;
 
 	if (!h1_get_buf(h1c, &h1c->obuf)) {
@@ -1821,10 +1820,10 @@
 			total += count;
 			if (last_data) {
 				h1m->state = H1_MSG_DONE;
-				if (h1c->flags & H1C_F_RX_BLK) {
-					h1c->flags &= ~H1C_F_RX_BLK;
+				if (h1s->flags & H1S_F_RX_BLK) {
+					h1s->flags &= ~H1S_F_RX_BLK;
 					h1_wake_stream_for_recv(h1s);
-					TRACE_STATE("Re-enable input processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+					TRACE_STATE("Re-enable input processing", H1_EV_TX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 				}
 
 				TRACE_USER((!(h1m->flags & H1_MF_RESP) ? "H1 request fully xferred" : "H1 response fully xferred"),
@@ -1839,7 +1838,7 @@
 
 	tmp.data = 0;
 	tmp.size = b_room(&h1c->obuf);
-	while (count && !(h1s->flags & H1S_F_PROCESSING_ERROR) && !(h1c->flags & H1C_F_TX_BLK) && blk) {
+	while (count && !(h1s->flags & (H1S_F_PROCESSING_ERROR|H1S_F_TX_BLK)) && blk) {
 		struct htx_sl *sl;
 		struct ist n, v;
 		enum htx_blk_type type = htx_get_blk_type(blk);
@@ -1869,10 +1868,10 @@
 				h1m->state = H1_MSG_HDR_FIRST;
 				if (h1s->meth == HTTP_METH_HEAD)
 					h1s->flags |= H1S_F_BODYLESS_RESP;
-				if (h1c->flags & H1C_F_RX_BLK) {
-					h1c->flags &= ~H1C_F_RX_BLK;
+				if (h1s->flags & H1S_F_RX_BLK) {
+					h1s->flags &= ~H1S_F_RX_BLK;
 					h1_wake_stream_for_recv(h1s);
-					TRACE_STATE("Re-enable input processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+					TRACE_STATE("Re-enable input processing", H1_EV_TX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 				}
 				break;
 
@@ -2213,8 +2212,8 @@
 
 				h1m->state = H1_MSG_DONE;
 				if (!(h1m->flags & H1_MF_RESP) && h1s->meth == HTTP_METH_CONNECT) {
-					h1c->flags |= H1C_F_TX_BLK;
-					TRACE_STATE("Disable output processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK, h1c->conn, h1s);
+					h1s->flags |= H1S_F_TX_BLK;
+					TRACE_STATE("Disable output processing", H1_EV_TX_DATA|H1_EV_H1S_BLK, h1c->conn, h1s);
 				}
 				else if ((h1m->flags & H1_MF_RESP) &&
 					 ((h1s->meth == HTTP_METH_CONNECT && h1s->status >= 200 && h1s->status < 300) || h1s->status == 101)) {
@@ -2225,10 +2224,10 @@
 					TRACE_STATE("switch H1 response in tunnel mode", H1_EV_TX_DATA|H1_EV_TX_HDRS, h1c->conn, h1s);
 				}
 
-				if (h1c->flags & H1C_F_RX_BLK) {
-					h1c->flags &= ~H1C_F_RX_BLK;
+				if (h1s->flags & H1S_F_RX_BLK) {
+					h1s->flags &= ~H1S_F_RX_BLK;
 					h1_wake_stream_for_recv(h1s);
-					TRACE_STATE("Re-enable input processing on h1c", H1_EV_TX_DATA|H1_EV_H1C_BLK|H1_EV_H1C_WAKE, h1c->conn, h1s);
+					TRACE_STATE("Re-enable input processing", H1_EV_TX_DATA|H1_EV_H1S_BLK|H1_EV_STRM_WAKE, h1c->conn, h1s);
 				}
 
 				TRACE_USER((!(h1m->flags & H1_MF_RESP) ? "H1 request fully xferred" : "H1 response fully xferred"),
@@ -2608,7 +2607,7 @@
 	}
 
   end:
-	if (!(h1c->flags & (H1C_F_OUT_FULL|H1C_F_TX_BLK)))
+	if (!(h1c->flags & H1C_F_OUT_FULL))
 		h1_wake_stream_for_send(h1c->h1s);
 
 	/* We're done, no more to send */