diff --git a/src/xprt_quic.c b/src/xprt_quic.c
index 96b6a47..f58715c 100644
--- a/src/xprt_quic.c
+++ b/src/xprt_quic.c
@@ -2101,7 +2101,7 @@
 			/* Special case for Initial packets: when they have all
 			 * been sent, select the next level.
 			 */
-			if (tel == QUIC_TLS_ENC_LEVEL_INITIAL &&
+			if ((tel == QUIC_TLS_ENC_LEVEL_INITIAL || tel == QUIC_TLS_ENC_LEVEL_HANDSHAKE) &&
 			    (MT_LIST_ISEMPTY(&qel->pktns->tx.frms) || qc->els[next_tel].pktns->tx.in_flight)) {
 				tel = next_tel;
 				qel = &qc->els[tel];