diff --git a/lib/dp-packet.h b/lib/dp-packet.h
index 770ddc1b952..2fa17d81402 100644
--- a/lib/dp-packet.h
+++ b/lib/dp-packet.h
@@ -1386,8 +1386,8 @@ dp_packet_ip_checksum_bad(const struct dp_packet *p)
 
 /* Return 'true' is packet 'b' is not encapsulated and is marked for IPv4
  * checksum offload, or if 'b' is encapsulated and the outer layer is marked
- * for IPv4 checksum offload. IPv6 packets and non offloaded packets return
- * 'false'. */
+ * for IPv4 checksum offload. IPv6 packets, non offloaded packets, and IPv4
+ * packets that are marked as good return 'false'. */
 static inline bool
 dp_packet_hwol_l3_csum_ipv4_ol(const struct dp_packet *b)
 {
@@ -1400,6 +1400,21 @@ dp_packet_hwol_l3_csum_ipv4_ol(const struct dp_packet *b)
     return false;
 }
 
+/* Return 'true' is packet 'b' is not encapsulated and is marked for IPv4
+ * checksum offload, or if 'b' is encapsulated and the outer layer is marked
+ * for IPv4 checksum offload. IPv6 packets and non offloaded packets return
+ * 'false'. */
+static inline bool
+dp_packet_hwol_l3_ipv4(const struct dp_packet *b)
+{
+    if (dp_packet_hwol_is_outer_ipv4(b)) {
+        return true;
+    } else if (!dp_packet_hwol_is_outer_ipv6(b)) {
+        return dp_packet_hwol_tx_ip_csum(b);
+    }
+    return false;
+}
+
 /* Calculate and set the IPv4 header checksum in packet 'p'. */
 static inline void
 dp_packet_ip_set_header_csum(struct dp_packet *p, bool inner)
diff --git a/lib/netdev-native-tnl.c b/lib/netdev-native-tnl.c
index 0d6d803fe45..dee9ab344e4 100644
--- a/lib/netdev-native-tnl.c
+++ b/lib/netdev-native-tnl.c
@@ -91,8 +91,7 @@ netdev_tnl_ip_extract_tnl_md(struct dp_packet *packet, struct flow_tnl *tnl,
 
         /* A packet coming from a network device might have the
          * csum already checked. In this case, skip the check. */
-        if (OVS_UNLIKELY(!dp_packet_ip_checksum_good(packet))
-            && !dp_packet_hwol_tx_ip_csum(packet)) {
+        if (OVS_UNLIKELY(!dp_packet_hwol_l3_csum_ipv4_ol(packet))) {
             if (csum(ip, IP_IHL(ip->ip_ihl_ver) * 4)) {
                 VLOG_WARN_RL(&err_rl, "ip packet has invalid checksum");
                 return NULL;
@@ -299,6 +298,13 @@ dp_packet_tnl_ol_process(struct dp_packet *packet,
                                          (char *) dp_packet_eth(packet) +
                                          VXLAN_HLEN);
         }
+    } else {
+        /* Mark non-l4 packets as tunneled. */
+        if (data->tnl_type == OVS_VPORT_TYPE_GENEVE) {
+            dp_packet_hwol_set_tunnel_geneve(packet);
+        } else if (data->tnl_type == OVS_VPORT_TYPE_VXLAN) {
+            dp_packet_hwol_set_tunnel_vxlan(packet);
+        }
     }
 }
 
diff --git a/lib/packets.c b/lib/packets.c
index 36c6692e5c6..5803d26f4ac 100644
--- a/lib/packets.c
+++ b/lib/packets.c
@@ -1149,7 +1149,7 @@ packet_set_ipv4_addr(struct dp_packet *packet,
         }
     }
 
-    if (dp_packet_hwol_tx_ip_csum(packet)) {
+    if (dp_packet_hwol_l3_ipv4(packet)) {
         dp_packet_ol_reset_ip_csum_good(packet);
     } else {
         nh->ip_csum = recalc_csum32(nh->ip_csum, old_addr, new_addr);
@@ -1328,7 +1328,7 @@ packet_set_ipv4(struct dp_packet *packet, ovs_be32 src, ovs_be32 dst,
     if (nh->ip_tos != tos) {
         uint8_t *field = &nh->ip_tos;
 
-        if (dp_packet_hwol_tx_ip_csum(packet)) {
+        if (dp_packet_hwol_l3_ipv4(packet)) {
             dp_packet_ol_reset_ip_csum_good(packet);
         } else {
             nh->ip_csum = recalc_csum16(nh->ip_csum, htons((uint16_t) *field),
@@ -1341,7 +1341,7 @@ packet_set_ipv4(struct dp_packet *packet, ovs_be32 src, ovs_be32 dst,
     if (nh->ip_ttl != ttl) {
         uint8_t *field = &nh->ip_ttl;
 
-        if (dp_packet_hwol_tx_ip_csum(packet)) {
+        if (dp_packet_hwol_l3_ipv4(packet)) {
             dp_packet_ol_reset_ip_csum_good(packet);
         } else {
             nh->ip_csum = recalc_csum16(nh->ip_csum, htons(*field << 8),
@@ -1979,7 +1979,7 @@ IP_ECN_set_ce(struct dp_packet *pkt, bool is_ipv6)
 
         tos |= IP_ECN_CE;
         if (nh->ip_tos != tos) {
-            if (dp_packet_hwol_tx_ip_csum(pkt)) {
+            if (dp_packet_hwol_l3_ipv4(pkt)) {
                 dp_packet_ol_reset_ip_csum_good(pkt);
             } else {
                 nh->ip_csum = recalc_csum16(nh->ip_csum, htons(nh->ip_tos),