diff --git a/src/mux_h2.c b/src/mux_h2.c
index 57f1dfe0a..43248f2cb 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -2086,6 +2086,15 @@ static int h2_wake(struct connection *conn)
 {
 	struct h2c *h2c = conn->mux_ctx;
 
+	/*
+	 * If we received early data, try to wake any stream, just in case
+	 * at least one of them was waiting for the handshake
+	 */
+	if ((conn->flags & (CO_FL_EARLY_SSL_HS | CO_FL_EARLY_DATA | CO_FL_HANDSHAKE)) ==
+	    CO_FL_EARLY_DATA) {
+		h2_wake_some_streams(h2c, 0, 0);
+		conn->flags &= ~CO_FL_EARLY_DATA;
+	}
 	if (conn->flags & CO_FL_ERROR || conn_xprt_read0_pending(conn) ||
 	    h2c->st0 == H2_CS_ERROR2 || h2c->flags & H2_CF_GOAWAY_FAILED ||
 	    (eb_is_empty(&h2c->streams_by_id) && h2c->last_sid >= 0 &&
diff --git a/src/mux_pt.c b/src/mux_pt.c
index cd3a28b42..71bb47775 100644
--- a/src/mux_pt.c
+++ b/src/mux_pt.c
@@ -51,6 +51,12 @@ static int mux_pt_wake(struct connection *conn)
 
 	ret = cs->data_cb->wake ? cs->data_cb->wake(cs) : 0;
 
+	/* If we had early data, and we're done with the handshake
+	 * then whe know the data are safe, and we can remove the flag.
+	 */
+	if ((conn->flags & (CO_FL_EARLY_DATA | CO_FL_EARLY_SSL_HS | CO_FL_HANDSHAKE)) ==
+	    CO_FL_EARLY_DATA)
+		conn->flags &= ~CO_FL_EARLY_DATA;
 	if (ret >= 0)
 		cs_update_mux_polling(cs);
 	return ret;
diff --git a/src/stream_interface.c b/src/stream_interface.c
index c2e3fffd4..6f9f27b98 100644
--- a/src/stream_interface.c
+++ b/src/stream_interface.c
@@ -585,7 +585,6 @@ static int si_cs_wake_cb(struct conn_stream *cs)
 	 * the handshake.
 	 */
 	if ((conn->flags & (CO_FL_EARLY_DATA | CO_FL_EARLY_SSL_HS)) == CO_FL_EARLY_DATA) {
-		conn->flags &= ~CO_FL_EARLY_DATA;
 		task_wakeup(si_task(si), TASK_WOKEN_MSG);
 	}