diff --git a/include/proto/h1.h b/include/proto/h1.h
index e6a4204ff..fb040d138 100644
--- a/include/proto/h1.h
+++ b/include/proto/h1.h
@@ -150,7 +150,6 @@ static inline const char *h1m_state_str(enum h1_state msg_state)
 	case H1_MSG_HDR_L2_LF:   return "MSG_HDR_L2_LF";
 	case H1_MSG_HDR_L2_LWS:  return "MSG_HDR_L2_LWS";
 	case H1_MSG_LAST_LF:     return "MSG_LAST_LF";
-	case H1_MSG_BODY:        return "MSG_BODY";
 	case H1_MSG_CHUNK_SIZE:  return "MSG_CHUNK_SIZE";
 	case H1_MSG_DATA:        return "MSG_DATA";
 	case H1_MSG_CHUNK_CRLF:  return "MSG_CHUNK_CRLF";
diff --git a/include/types/h1.h b/include/types/h1.h
index c6c97dcbd..26eafd339 100644
--- a/include/types/h1.h
+++ b/include/types/h1.h
@@ -120,21 +120,17 @@ enum h1m_state {
 	H1_MSG_HDR_L2_LF    = 23, // parsing header LWS (LF) inside/after value
 	H1_MSG_HDR_L2_LWS   = 24, // checking whether it's a new header or an LWS
 
-	H1_MSG_LAST_LF      = 25, // parsing last LF
+	H1_MSG_LAST_LF      = 25, // parsing last LF, last state for headers
 
-	/* Body processing.
-	 * The state H1_MSG_BODY is a delimiter to know if we're waiting for headers
-	 * or body. All the sub-states below also indicate we're processing the body,
-	 * with some additional information.
-	 */
-	H1_MSG_BODY         = 26, // parsing body at end of headers
-	H1_MSG_CHUNK_SIZE   = 27, // parsing the chunk size (RFC7230 #4.1)
-	H1_MSG_DATA         = 28, // skipping data chunk / content-length data
-	H1_MSG_CHUNK_CRLF   = 29, // skipping CRLF after data chunk
-	H1_MSG_TRAILERS     = 30, // trailers (post-data entity headers)
+	/* Body processing. */
+
+	H1_MSG_CHUNK_SIZE   = 26, // parsing the chunk size (RFC7230 #4.1)
+	H1_MSG_DATA         = 27, // skipping data chunk / content-length data
+	H1_MSG_CHUNK_CRLF   = 28, // skipping CRLF after data chunk
+	H1_MSG_TRAILERS     = 29, // trailers (post-data entity headers)
 	/* we enter this state when we've received the end of the current message */
-	H1_MSG_DONE         = 31, // message end received, waiting for resync or close
-	H1_MSG_TUNNEL       = 32, // tunneled data after DONE
+	H1_MSG_DONE         = 30, // message end received, waiting for resync or close
+	H1_MSG_TUNNEL       = 31, // tunneled data after DONE
 } __attribute__((packed));
 
 
diff --git a/src/h1.c b/src/h1.c
index d88408efe..fc0b8da58 100644
--- a/src/h1.c
+++ b/src/h1.c
@@ -1073,7 +1073,21 @@ int h1_headers_to_hdr_list(char *start, const char *stop,
 			}
 			http_set_hdr(&hdr[hdr_count++], ist(""), ist(""));
 		}
-		state = H1_MSG_BODY;
+
+		/* reaching here we've parsed the whole message. We may detect
+		 * that we were already continuing an interrupted parsing pass
+		 * so we were silently looking for the end of message not
+		 * updating anything before deciding to parse it fully at once.
+		 * It's guaranteed that we won't match this test twice in a row
+		 * since restarting will turn zero.
+		 */
+		if (restarting)
+			goto restart;
+
+		if (h1m->flags & H1_MF_CHNK)
+			state = H1_MSG_CHUNK_SIZE;
+		else
+			state = H1_MSG_DATA;
 		break;
 
 	default:
@@ -1081,14 +1095,9 @@ int h1_headers_to_hdr_list(char *start, const char *stop,
 		goto http_msg_invalid;
 	}
 
-	/* reaching here, we've parsed the whole message and the state is
-	 * H1_MSG_BODY. We may discover that we were already continuing an
-	 * interrupted parsing session, thus we were silently looking for
-	 * the end of message before deciding to parse it fully at once.
-	 * We won't come there again since restarting will turn zero.
+	/* Now we've left the headers state and are either in H1_MSG_DATA or
+	 * H1_MSG_CHUNK_SIZE.
 	 */
-	if (restarting)
-		goto restart;
 
 	if (slp && !skip_update)
 		*slp = sl;
diff --git a/src/mux_h2.c b/src/mux_h2.c
index d842cd8d2..922cabefe 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -3237,8 +3237,8 @@ static size_t h2s_frt_make_resp_headers(struct h2s *h2s, const struct buffer *bu
 		h1m->err_pos = -1; // don't care about errors on the response path
 		goto end;
 	}
-	else
-		h1m->state = (h1m->flags & H1_MF_CHNK) ? H1_MSG_CHUNK_SIZE : H1_MSG_BODY;
+
+	/* now the h1m state is either H1_MSG_CHUNK_SIZE or H1_MSG_DATA */
 
  end:
 	//fprintf(stderr, "[%d] sent simple H2 response (sid=%d) = %d bytes (%d in, ep=%u, es=%s)\n", h2c->st0, h2s->id, outbuf.len, ret, h1m->err_pos, h1_msg_state_str(h1m->err_state));
@@ -3568,7 +3568,7 @@ static size_t h2_snd_buf(struct conn_stream *cs, struct buffer *buf, size_t coun
 		h2s->flags |= H2_SF_OUTGOING_DATA;
 
 	while (h2s->h1m.state < H1_MSG_DONE && count) {
-		if (h2s->h1m.state < H1_MSG_BODY) {
+		if (h2s->h1m.state <= H1_MSG_LAST_LF) {
 			ret = h2s_frt_make_resp_headers(h2s, buf, total, count);
 		}
 		else if (h2s->h1m.state < H1_MSG_TRAILERS) {