--- a/dom/system/gonk/RadioInterfaceLayer.js
+++ b/dom/system/gonk/RadioInterfaceLayer.js
@@ -999,19 +999,22 @@ RadioInterfaceLayer.prototype = {
     let mwi = message.mwi;
     if (mwi) {
       mwi.returnNumber = message.sender || null;
       mwi.returnMessage = message.fullBody || null;
       ppmm.broadcastAsyncMessage("RIL:VoicemailNotification", mwi);
       return;
     }
 
-    let id = gSmsDatabaseService.saveReceivedMessage(message.sender || null,
-                                                     message.fullBody || null,
-                                                     message.timestamp);
+    let id = -1;
+    if (message.messageClass != RIL.PDU_DCS_MSG_CLASS_0) {
+      id = gSmsDatabaseService.saveReceivedMessage(message.sender || null,
+                                                   message.fullBody || null,
+                                                   message.timestamp);
+    }
     let sms = gSmsService.createSmsMessage(id,
                                            DOM_SMS_DELIVERY_RECEIVED,
                                            message.sender || null,
                                            message.receiver || null,
                                            message.fullBody || null,
                                            message.timestamp,
                                            false);
 

--- a/dom/system/gonk/ril_worker.js
+++ b/dom/system/gonk/ril_worker.js
@@ -3079,16 +3079,25 @@ let RIL = {
 
     if (message.epid == PDU_PID_SHORT_MESSAGE_TYPE_0) {
       // `A short message type 0 indicates that the ME must acknowledge receipt
       // of the short message but shall discard its contents.` ~ 3GPP TS 23.040
       // 9.2.3.9
       return PDU_FCS_OK;
     }
 
+    // TODO: Bug 739143: B2G SMS: Support SMS Storage Full event
+    if ((message.messageClass != PDU_DCS_MSG_CLASS_0) && !true) {
+      // `When a mobile terminated message is class 0..., the MS shall display
+      // the message immediately and send a ACK to the SC ..., irrespective of
+      // whether there is memory available in the (U)SIM or ME.` ~ 3GPP 23.038
+      // clause 4.
+      return PDU_FCS_UNSPECIFIED;
+    }
+
     if (message.header && (message.header.segmentMaxSeq > 1)) {
       message = this._processReceivedSmsSegment(message);
     } else {
       if (message.encoding == PDU_DCS_MSG_CODING_8BITS_ALPHABET) {
         message.fullData = message.data;
         delete message.data;
       } else {
         message.fullBody = message.body;