diff --git a/src/h3.c b/src/h3.c
index a94b24b64..602627f61 100644
--- a/src/h3.c
+++ b/src/h3.c
@@ -534,8 +534,7 @@ static int h3_resp_data_send(struct qcs *qcs, struct buffer *buf, size_t count)
 	struct buffer *res;
 	size_t total = 0;
 	struct htx *htx;
-	int bsize, fsize;
-	int frame_length_size;  /* size in bytes of frame length varint field */
+	int bsize, fsize, hsize;
 	struct htx_blk *blk;
 	enum htx_blk_type type;
 
@@ -557,19 +556,34 @@ static int h3_resp_data_send(struct qcs *qcs, struct buffer *buf, size_t count)
 	if (fsize > count)
 		fsize = count;
 
-	frame_length_size = quic_int_getsize(fsize);
+	/* h3 DATA headers : 1-byte frame type + varint frame length */
+	hsize = 1 + QUIC_VARINT_MAX_SIZE;
 
-	b_reset(&outbuf);
-	outbuf = b_make(b_tail(res), b_contig_space(res), 0, 0);
+	while (1) {
+		b_reset(&outbuf);
+		outbuf = b_make(b_tail(res), b_contig_space(res), 0, 0);
+		if (b_size(&outbuf) > hsize || !b_space_wraps(res))
+			break;
+		b_slow_realign(res, trash.area, b_data(res));
+	}
 
-	if (1 + fsize + frame_length_size > b_room(&outbuf))
-		ABORT_NOW();
+	/* not enough room for headers and at least one data byte, block the
+	 * stream
+	 */
+	if (b_size(&outbuf) <= hsize) {
+		qcs->flags |= QC_SF_BLK_MROOM;
+		goto end;
+	}
 
-	b_putchr(&outbuf, 0x00); /* h3 frame type = DATA */
-	b_quic_enc_int(&outbuf, fsize);
+	if (b_size(&outbuf) < hsize + fsize)
+		fsize = b_size(&outbuf) - hsize;
+	BUG_ON(fsize <= 0);
+
+	b_putchr(&outbuf, 0x00);        /* h3 frame type = DATA */
+	b_quic_enc_int(&outbuf, fsize); /* h3 frame length */
 
-	total += fsize;
 	b_putblk(&outbuf, htx_get_blk_ptr(htx, blk), fsize);
+	total += fsize;
 	count -= fsize;
 
 	if (fsize == bsize)
@@ -577,6 +591,7 @@ static int h3_resp_data_send(struct qcs *qcs, struct buffer *buf, size_t count)
 	else
 		htx_cut_data_blk(htx, blk, fsize);
 
+	/* commit the buffer */
 	b_add(res, b_data(&outbuf));
 	goto new_frame;
 
@@ -597,7 +612,7 @@ size_t h3_snd_buf(struct conn_stream *cs, struct buffer *buf, size_t count, int
 
 	htx = htx_from_buf(buf);
 
-	while (count && !htx_is_empty(htx)) {
+	while (count && !htx_is_empty(htx) && !(qcs->flags & QC_SF_BLK_MROOM)) {
 		idx = htx_get_head(htx);
 		blk = htx_get_blk(htx, idx);
 		btype = htx_get_blk_type(blk);
@@ -643,10 +658,13 @@ size_t h3_snd_buf(struct conn_stream *cs, struct buffer *buf, size_t count, int
 
 	if ((htx->flags & HTX_FL_EOM) && htx_is_empty(htx))
 		qcs->flags |= QC_SF_FIN_STREAM;
-	// TODO should I call the mux directly here ?
-	qc_snd_buf(cs, buf, total, flags);
 
  out:
+	if (total) {
+		if (!(qcs->qcc->wait_event.events & SUB_RETRY_SEND))
+			tasklet_wakeup(qcs->qcc->wait_event.tasklet);
+	}
+
 	return total;
 }
 
diff --git a/src/mux_quic.c b/src/mux_quic.c
index 710aa0e63..55a4dc557 100644
--- a/src/mux_quic.c
+++ b/src/mux_quic.c
@@ -1350,7 +1350,7 @@ static int qcs_push_frame(struct qcs *qcs, struct buffer *payload, int fin, uint
 static int qc_send(struct qcc *qcc)
 {
 	struct eb64_node *node;
-	int ret, done;
+	int ret, done, xprt_wake = 0;
 
 	TRACE_ENTER(QC_EV_QCC_SEND, qcc->conn);
 	ret = done = 0;
@@ -1380,18 +1380,26 @@ static int qc_send(struct qcc *qcc)
 			if (ret < 0)
 				ABORT_NOW();
 
+			if (ret > 0) {
+				xprt_wake = 1;
+				if (qcs->flags & QC_SF_BLK_MROOM) {
+					qcs->flags &= ~QC_SF_BLK_MROOM;
+					qcs_notify_send(qcs);
+				}
+			}
+
 			qcs->tx.offset += ret;
+
 			if (b_data(buf)) {
 				qcc->conn->xprt->subscribe(qcc->conn, qcc->conn->xprt_ctx,
 				                           SUB_RETRY_SEND, &qcc->wait_event);
-				break;
 			}
 		}
 		node = eb64_next(node);
 	}
-	if (ret > 0)
-		tasklet_wakeup(((struct ssl_sock_ctx *)(qcc->conn->xprt_ctx))->wait_event.tasklet);
 
+	if (xprt_wake)
+		tasklet_wakeup(((struct ssl_sock_ctx *)(qcc->conn->xprt_ctx))->wait_event.tasklet);
 
 	TRACE_LEAVE(QC_EV_QCC_SEND, qcc->conn);
 	return 0;
@@ -1834,25 +1842,6 @@ static size_t qc_rcv_buf(struct conn_stream *cs, struct buffer *buf, size_t coun
 	return ret;
 }
 
-/* Called from the upper layer, to send data from buffer <buf> for no more than
- * <count> bytes. Returns the number of bytes effectively sent. Some status
- * flags may be updated on the conn_stream.
- */
-size_t qc_snd_buf(struct conn_stream *cs, struct buffer *buf, size_t count, int flags)
-{
-	struct qcs *qcs = cs->ctx;
-
-	TRACE_ENTER(QC_EV_QCS_SEND|QC_EV_STRM_SEND, qcs->qcc->conn, qcs);
-
-	if (count) {
-		if (!(qcs->qcc->wait_event.events & SUB_RETRY_SEND))
-			tasklet_wakeup(qcs->qcc->wait_event.tasklet);
-	}
-
-	TRACE_LEAVE(QC_EV_QCS_SEND|QC_EV_STRM_SEND, qcs->qcc->conn, qcs);
-	return count;
-}
-
 /* Called from the upper layer, to send data from buffer <buf> for no more than
  * <count> bytes. Returns the number of bytes effectively sent. Some status
  * flags may be updated on the mux.