Packet network addresses, such as Internet Protocol addresses, may be assigned dynamically to computer systems accessed from the packet network by dial-out calls through a telephone network. A dial-out destination system will have an assigned name, typically a domain name. In response to a request for translation of the name, a network access server capable of reaching the destination obtains or assigns an address on a temporary basis. The network access server initiates the call to the destination system through the telephone network. The system initiating communication to the destination system uses the assigned address in any subsequent packet data communications. When the communication ends, the address is again available for a new assignment. This approach provides a dynamic address assignment technique for use on dial-out access services.