diff --git a/src/llc.c b/src/llc.c
index 700585a..c8d74d8 100644
--- a/src/llc.c
+++ b/src/llc.c
@@ -96,19 +96,40 @@
 
 void llc_queue_init(struct gprs_llc_queue *q)
 {
-	INIT_LLIST_HEAD(&q->queue);
+	unsigned int i;
+
 	q->queue_size = 0;
 	q->queue_octets = 0;
 	q->avg_queue_delay = 0;
+	for (i = 0; i < ARRAY_SIZE(q->queue); i++)
+		INIT_LLIST_HEAD(&q->queue[i]);
 }
 
 
+static enum gprs_llc_queue_prio llc_sapi2prio(uint8_t sapi)
+{
+	switch (sapi) {
+	case 1:
+		return LLC_QUEUE_PRIO_GMM;
+	case 2:
+	case 7:
+	case 8:
+		return LLC_QUEUE_PRIO_TOM_SMS;
+	default:
+		return LLC_QUEUE_PRIO_OTHER;
+	}
+}
+
 void llc_queue_enqueue(struct gprs_llc_queue *q, struct msgb *llc_msg, const struct timespec *expire_time)
 {
 	struct MetaInfo *meta_storage;
+	struct gprs_llc_hdr *llc_hdr = (struct gprs_llc_hdr *)msgb_data(llc_msg);
+	enum gprs_llc_queue_prio prio;
 
 	osmo_static_assert(sizeof(*meta_storage) <= sizeof(llc_msg->cb), info_does_not_fit);
 
+	prio = llc_sapi2prio(llc_hdr->sapi);
+
 	q->queue_size += 1;
 	q->queue_octets += msgb_length(llc_msg);
 
@@ -116,17 +137,20 @@
 	osmo_clock_gettime(CLOCK_MONOTONIC, &meta_storage->recv_time);
 	meta_storage->expire_time = *expire_time;
 
-	msgb_enqueue(&q->queue, llc_msg);
+	msgb_enqueue(&q->queue[prio], llc_msg);
 }
 
 void llc_queue_clear(struct gprs_llc_queue *q, struct gprs_rlcmac_bts *bts)
 {
 	struct msgb *msg;
+	unsigned int i;
 
-	while ((msg = msgb_dequeue(&q->queue))) {
-		if (bts)
-			bts_do_rate_ctr_inc(bts, CTR_LLC_FRAME_DROPPED);
-		msgb_free(msg);
+	for (i = 0; i < ARRAY_SIZE(q->queue); i++) {
+		while ((msg = msgb_dequeue(&q->queue[i]))) {
+			if (bts)
+				bts_do_rate_ctr_inc(bts, CTR_LLC_FRAME_DROPPED);
+			msgb_free(msg);
+		}
 	}
 
 	q->queue_size = 0;
@@ -137,51 +161,53 @@
 {
 	struct msgb *msg, *msg1 = NULL, *msg2 = NULL;
 	struct llist_head new_queue;
+	unsigned int i;
 	size_t queue_size = 0;
 	size_t queue_octets = 0;
 	INIT_LLIST_HEAD(&new_queue);
 
-	while (1) {
-		if (msg1 == NULL)
-			msg1 = msgb_dequeue(&q->queue);
+	for (i = 0; i < ARRAY_SIZE(q->queue); i++) {
+		while (1) {
+			if (msg1 == NULL)
+				msg1 = msgb_dequeue(&q->queue[i]);
 
-		if (msg2 == NULL)
-			msg2 = msgb_dequeue(&o->queue);
+			if (msg2 == NULL)
+				msg2 = msgb_dequeue(&o->queue[i]);
 
-		if (msg1 == NULL && msg2 == NULL)
-			break;
+			if (msg1 == NULL && msg2 == NULL)
+				break;
 
-		if (msg1 == NULL) {
-			msg = msg2;
-			msg2 = NULL;
-		} else if (msg2 == NULL) {
-			msg = msg1;
-			msg1 = NULL;
-		} else {
-			const struct MetaInfo *mi1 = (struct MetaInfo *)&msg1->cb[0];
-			const struct MetaInfo *mi2 = (struct MetaInfo *)&msg2->cb[0];
-
-			if (timespeccmp(&mi2->recv_time, &mi1->recv_time, >)) {
+			if (msg1 == NULL) {
+				msg = msg2;
+				msg2 = NULL;
+			} else if (msg2 == NULL) {
 				msg = msg1;
 				msg1 = NULL;
 			} else {
-				msg = msg2;
-				msg2 = NULL;
+				const struct MetaInfo *mi1 = (struct MetaInfo *)&msg1->cb[0];
+				const struct MetaInfo *mi2 = (struct MetaInfo *)&msg2->cb[0];
+
+				if (timespeccmp(&mi2->recv_time, &mi1->recv_time, >)) {
+					msg = msg1;
+					msg1 = NULL;
+				} else {
+					msg = msg2;
+					msg2 = NULL;
+				}
 			}
+
+			msgb_enqueue(&new_queue, msg);
+			queue_size += 1;
+			queue_octets += msgb_length(msg);
 		}
 
-		msgb_enqueue(&new_queue, msg);
-		queue_size += 1;
-		queue_octets += msgb_length(msg);
+		OSMO_ASSERT(llist_empty(&q->queue[i]));
+		OSMO_ASSERT(llist_empty(&o->queue[i]));
+		llist_splice_init(&new_queue, &q->queue[i]);
 	}
 
-	OSMO_ASSERT(llist_empty(&q->queue));
-	OSMO_ASSERT(llist_empty(&o->queue));
-
 	o->queue_size = 0;
 	o->queue_octets = 0;
-
-	llist_splice_init(&new_queue, &q->queue);
 	q->queue_size = queue_size;
 	q->queue_octets = queue_octets;
 }
@@ -193,9 +219,13 @@
 	struct msgb *msg;
 	struct timespec *tv, tv_now, tv_result;
 	uint32_t lifetime;
+	unsigned int i;
 	const struct MetaInfo *meta_storage;
 
-	msg = msgb_dequeue(&q->queue);
+	for (i = 0; i < ARRAY_SIZE(q->queue); i++) {
+		if ((msg = msgb_dequeue(&q->queue[i])))
+			break;
+	}
 	if (!msg)
 		return NULL;
 
diff --git a/src/llc.h b/src/llc.h
index bd542c0..adfab65 100644
--- a/src/llc.h
+++ b/src/llc.h
@@ -1,4 +1,4 @@
-/*
+/* 3GPP TS 44.064
  * Copyright (C) 2013 by Holger Hans Peter Freyther
  * Copyright (C) 2022 by by Sysmocom s.f.m.c. GmbH
  *
@@ -23,13 +23,30 @@
 #include <string.h>
 #include <time.h>
 
+#include <osmocom/core/endian.h>
 #include <osmocom/core/linuxlist.h>
 #include <osmocom/core/msgb.h>
+#include <osmocom/core/endian.h>
 
 #define LLC_MAX_LEN 1543
 
 struct gprs_rlcmac_bts;
 
+struct gprs_llc_hdr {
+#if OSMO_IS_LITTLE_ENDIAN
+	union { /* 5.2, 6.2.0 */
+		uint8_t address;
+		uint8_t sapi:4, unused:2, c_r:1, pd:1;
+#elif OSMO_IS_BIG_ENDIAN
+/* auto-generated from the little endian part above (libosmocore/contrib/struct_endianess.py) */
+	union {
+		uint8_t address;
+		uint8_t pd:1, c_r:1, unused:2, sapi:4;
+#endif
+	};
+	uint8_t control[0];
+} __attribute__ ((packed));
+
 /**
  * I represent the LLC data to a MS
  */
@@ -87,11 +104,17 @@
 /**
  * I store the LLC frames that come from the SGSN.
  */
+enum gprs_llc_queue_prio { /* lowest value has highest prio */
+	LLC_QUEUE_PRIO_GMM = 0, /* SAPI 1 */
+	LLC_QUEUE_PRIO_TOM_SMS, /* SAPI 2,7,8 */
+	LLC_QUEUE_PRIO_OTHER, /* Other SAPIs */
+	_LLC_QUEUE_PRIO_SIZE /* used to calculate size of enum */
+};
 struct gprs_llc_queue {
 	uint32_t avg_queue_delay; /* Average delay of data going through the queue */
 	size_t queue_size;
 	size_t queue_octets;
-	struct llist_head queue; /* queued LLC DL data */
+	struct llist_head queue[_LLC_QUEUE_PRIO_SIZE]; /* queued LLC DL data. See enum gprs_llc_queue_prio. */
 };
 
 void llc_queue_calc_pdu_lifetime(struct gprs_rlcmac_bts *bts, const uint16_t pdu_delay_csec,