diff --git a/include/haproxy/stconn-t.h b/include/haproxy/stconn-t.h
index ce06a5cce..30f468ad7 100644
--- a/include/haproxy/stconn-t.h
+++ b/include/haproxy/stconn-t.h
@@ -37,6 +37,7 @@ enum iobuf_flags {
 	IOBUF_FL_INTERIM_FF       = 0x00000008, /* Producer side warn it will immediately retry a fast-forward.
 						 *  .done_fastfwd() on consumer side must take care of this flag
 						 */
+	IOBUF_FL_EOI              = 0x00000010, /* A EOI was encountered on producer side */
 };
 
 struct iobuf {
diff --git a/src/mux_h1.c b/src/mux_h1.c
index b022c0d01..51854f28a 100644
--- a/src/mux_h1.c
+++ b/src/mux_h1.c
@@ -4720,6 +4720,11 @@ static int h1_fastfwd(struct stconn *sc, unsigned int count, unsigned int flags)
 
 
 	sdo->iobuf.flags &= ~IOBUF_FL_INTERIM_FF;
+	if (se_fl_test(h1s->sd, SE_FL_EOI)) {
+		sdo->iobuf.flags |= IOBUF_FL_EOI; /* TODO: it may be good to have a flag to be sure we can
+						   *       forward the EOI the to consumer side
+						   */
+	}
 	se_done_ff(sdo);
 
 	ret = total;
diff --git a/src/mux_h2.c b/src/mux_h2.c
index ab5e3cf60..024f379ea 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -7041,21 +7041,8 @@ static size_t h2_done_ff(struct stconn *sc)
 		goto end;
 	head = b_peek(mbuf, b_data(mbuf) - sd->iobuf.data);
 
-	/* FIXME: Must be handled with a flag. It is just a temporary hack */
-	{
-		struct xref *peer;
-		struct sedesc *sdo;
-
-		peer = xref_get_peer_and_lock(&h2s->sd->xref);
-		if (!peer)
-			goto end;
-
-		sdo = container_of(peer, struct sedesc, xref);
-		xref_unlock(&h2s->sd->xref, peer);
-
-		if (se_fl_test(sdo, SE_FL_EOI))
-			h2s->flags &= ~H2_SF_MORE_HTX_DATA;
-	}
+	if (sd->iobuf.flags & IOBUF_FL_EOI)
+		h2s->flags &= ~H2_SF_MORE_HTX_DATA;
 
 	if (!(sd->iobuf.flags & IOBUF_FL_FF_BLOCKED) &&
 	    !(h2s->flags & H2_SF_BLK_SFCTL) &&