A wireless end-user device has wireless wide-area network (WWAN) and wireless local-area network (WLAN) modems. One or more processors associate each of a plurality of Internet access requests with a corresponding destination address. The processors apply a differential traffic control policy to at least some of the Internet access requests, based on the corresponding destination address and whether or not that destination address is covered by a differential traffic control policy list. For one of the modems, the list treatment of a destination address determines whether an Internet access request is allowed or disallowed. For the other modem, the list treatment does not cause that same destination address to cause an Internet access request to be disallowed.