diff --git a/include/common/htx.h b/include/common/htx.h
index 463f7299b..fd0871c52 100644
--- a/include/common/htx.h
+++ b/include/common/htx.h
@@ -186,7 +186,7 @@ struct htx_blk *htx_add_blk_type_size(struct htx *htx, enum htx_blk_type type, u
 struct htx_blk *htx_add_all_headers(struct htx *htx, const struct http_hdr *hdrs);
 struct htx_blk *htx_add_endof(struct htx *htx, enum htx_blk_type type);
 struct htx_blk *htx_add_data_atonce(struct htx *htx, const struct ist data);
-struct htx_blk *htx_add_data(struct htx *htx, const struct ist data);
+size_t htx_add_data(struct htx *htx, const struct ist data);
 struct htx_blk *htx_add_trailer(struct htx *htx, const struct ist tlr);
 struct htx_blk *htx_add_data_before(struct htx *htx, const struct htx_blk *ref, const struct ist data);
 
diff --git a/src/cache.c b/src/cache.c
index 83aacd136..e390b2168 100644
--- a/src/cache.c
+++ b/src/cache.c
@@ -957,8 +957,7 @@ static size_t htx_cache_dump_data(struct appctx *appctx, struct htx *htx,
 		sz = MIN(len, shctx->block_size - offset);
 		data = ist2((const char *)shblk->data + offset, sz);
 		if (type == HTX_BLK_DATA) {
-			if (!htx_add_data(htx, data))
-				break;
+			sz = htx_add_data(htx, data);
 		}
 		else { /* HTX_BLK_TLR */
 			if (!htx_add_trailer(htx, data))
@@ -968,7 +967,7 @@ static size_t htx_cache_dump_data(struct appctx *appctx, struct htx *htx,
 		offset += sz;
 		len -= sz;
 		total += sz;
-		if (!len)
+		if (!len || sz < data.len)
 			break;
 		offset = 0;
 	}
diff --git a/src/hlua.c b/src/hlua.c
index 3c9c70a78..a3fd57b91 100644
--- a/src/hlua.c
+++ b/src/hlua.c
@@ -4568,8 +4568,7 @@ __LJMP static int hlua_applet_htx_send_yield(lua_State *L, int status, lua_KCont
 		max = len - l;
 
 	/* Copy data. */
-	if (!htx_add_data(htx, ist2(data + l, max)))
-		goto snd_yield;
+	max = htx_add_data(htx, ist2(data + l, max));
 	channel_add_input(res, max);
 
 	/* update counters. */
diff --git a/src/http_htx.c b/src/http_htx.c
index b9501bed7..9892fd32a 100644
--- a/src/http_htx.c
+++ b/src/http_htx.c
@@ -657,9 +657,11 @@ static struct htx *http_str_to_htx(struct buffer *buf, struct ist raw)
 		goto error;
 	sl->info.res.status = h1sl.st.status;
 
-	if (raw.len > ret) {
-		if (!htx_add_data(htx, ist2(raw.ptr + ret, raw.len - ret)))
+	while (raw.len > ret) {
+		int sent = htx_add_data(htx, ist2(raw.ptr + ret, raw.len - ret));
+		if (!sent)
 			goto error;
+		ret += sent;
 	}
 	if (!htx_add_endof(htx, HTX_BLK_EOM))
 		goto error;
diff --git a/src/htx.c b/src/htx.c
index 2aeb077f2..32e23d115 100644
--- a/src/htx.c
+++ b/src/htx.c
@@ -758,11 +758,18 @@ struct htx_blk *htx_add_endof(struct htx *htx, enum htx_blk_type type)
 
 
 /* Adds an HTX block of type DATA in <htx>. It first tries to append data if
- * possible. It returns the new block on success. Otherwise, it returns NULL.
+ * possible. It returns the number of bytes consumed from <data>, which may be
+ * zero if nothing could be copied.
  */
-struct htx_blk *htx_add_data(struct htx *htx, const struct ist data)
+size_t htx_add_data(struct htx *htx, const struct ist data)
 {
-	return htx_add_data_atonce(htx, data);
+	struct htx_blk *blk;
+
+	blk = htx_add_data_atonce(htx, data);
+	if (blk)
+		return data.len;
+	else
+		return 0;
 }
 
 /* Adds an HTX block of type TLR in <htx>. It returns the new block on
diff --git a/src/mux_h1.c b/src/mux_h1.c
index d1e7c1d76..ef622bd2b 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -1143,6 +1143,8 @@ static size_t h1_process_data(struct h1s *h1s, struct h1m *h1m, struct htx *htx,
 				 *   => we can swap the buffers and place an htx header into
 				 *      the target buffer instead
 				 */
+				int32_t try = ret;
+
 				if (unlikely(htx_is_empty(htx) && ret == b_data(buf) &&
 					     !*ofs && b_head_ofs(buf) == sizeof(struct htx))) {
 					void *raw_area = buf->area;
@@ -1162,12 +1164,15 @@ static size_t h1_process_data(struct h1s *h1s, struct h1m *h1m, struct htx *htx,
 					 * empty pre-initialized HTX header
 					 */
 				}
-				else if (!htx_add_data(htx, ist2(b_peek(buf, *ofs), ret)))
-					goto end;
+				else {
+					ret = htx_add_data(htx, ist2(b_peek(buf, *ofs), try));
+				}
 				h1m->curr_len -= ret;
 				max -= sizeof(struct htx_blk) + ret;
 				*ofs += ret;
 				total += ret;
+				if (ret < try)
+					goto end;
 			}
 
 			if (!h1m->curr_len) {
@@ -1220,12 +1225,15 @@ static size_t h1_process_data(struct h1s *h1s, struct h1m *h1m, struct htx *htx,
 					ret = b_contig_data(buf, *ofs);
 
 				if (ret) {
-					if (!htx_add_data(htx, ist2(b_peek(buf, *ofs), ret)))
-						goto end;
+					int32_t try = ret;
+
+					ret = htx_add_data(htx, ist2(b_peek(buf, *ofs), try));
 					h1m->curr_len -= ret;
 					max -= sizeof(struct htx_blk) + ret;
 					*ofs += ret;
 					total += ret;
+					if (ret < try)
+						goto end;
 				}
 				if (!h1m->curr_len) {
 					h1m->state = H1_MSG_CHUNK_CRLF;
@@ -1291,11 +1299,14 @@ static size_t h1_process_data(struct h1s *h1s, struct h1m *h1m, struct htx *htx,
 			ret = b_contig_data(buf, *ofs);
 
 		if (ret) {
-			if (!htx_add_data(htx, ist2(b_peek(buf, *ofs), ret)))
-				goto end;
+			int32_t try = ret;
+
+			ret = htx_add_data(htx, ist2(b_peek(buf, *ofs), try));
 
 			*ofs += ret;
 			total = ret;
+			if (ret < try)
+				goto end;
 		}
 	}
 
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 6bec578b6..7d29a7d1f 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -3802,6 +3802,8 @@ try_again:
 	}
 
 	if (htx) {
+		unsigned int sent;
+
 		block1 = htx_free_data_space(htx);
 		if (!block1) {
 			h2c->flags |= H2_CF_DEM_SFULL;
@@ -3815,10 +3817,7 @@ try_again:
 		if (flen > block1)
 			flen = block1;
 
-		if (!htx_add_data(htx, ist2(b_head(&h2c->dbuf), flen))) {
-			h2c->flags |= H2_CF_DEM_SFULL;
-			goto fail;
-		}
+		sent = htx_add_data(htx, ist2(b_head(&h2c->dbuf), flen));
 
 		b_del(&h2c->dbuf, flen);
 		h2c->dfl    -= flen;
@@ -3829,6 +3828,12 @@ try_again:
 			h2s->body_len -= flen;
 			htx->extra = h2s->body_len;
 		}
+
+		if (sent < flen) {
+			h2c->flags |= H2_CF_DEM_SFULL;
+			goto fail;
+		}
+
 		goto try_again;
 	}
 	else if (unlikely(b_space_wraps(csbuf) &&
diff --git a/src/proto_htx.c b/src/proto_htx.c
index 0bb1eb2fd..27150a8ed 100644
--- a/src/proto_htx.c
+++ b/src/proto_htx.c
@@ -5502,7 +5502,18 @@ static int htx_reply_40x_unauthorized(struct stream *s, const char *auth_realm)
 		goto fail;
 	if (status == 407 && !htx_add_header(htx, ist("Proxy-Authenticate"), ist2(trash.area, trash.data)))
 		goto fail;
-	if (!htx_add_endof(htx, HTX_BLK_EOH) || !htx_add_data(htx, body) || !htx_add_endof(htx, HTX_BLK_EOM))
+	if (!htx_add_endof(htx, HTX_BLK_EOH))
+		goto fail;
+
+	while (body.len) {
+		size_t sent = htx_add_data(htx, body);
+		if (!sent)
+			goto fail;
+		body.ptr += sent;
+		body.len -= sent;
+	}
+
+	if (!htx_add_endof(htx, HTX_BLK_EOM))
 		goto fail;
 
 	data = htx->data - co_data(res);
diff --git a/src/stats.c b/src/stats.c
index 9c3bf7c14..4b994b72c 100644
--- a/src/stats.c
+++ b/src/stats.c
@@ -258,7 +258,7 @@ static int stats_putchk(struct channel *chn, struct htx *htx, struct buffer *chk
 	if (htx) {
 		if (chk->data >= channel_htx_recv_max(chn, htx))
 			return 0;
-		if (!htx_add_data(htx, ist2(chk->area, chk->data)))
+		if (!htx_add_data_atonce(htx, ist2(chk->area, chk->data)))
 			return 0;
 		channel_add_input(chn, chk->data);
 		chk->data = 0;