Network address translation (NAT) has become an important technology in the Internet, supporting scalable addressing, addressing autonomy, concealed endpoint identity, and transparent redirection. However, NAT currently lacks a well-specified scalable architecture and interferes with end-to-end security and reliability. In this paper, we present TRIAD as a NAT-based architecture that solves these problems. The key ideas of TRIAD are: i) basing all identification on DNS names, not end-to-end addresses, supported by a router-integrated directory service, ii) providing end-to-end semantics with a name-based transport-level pseudo-header, and, iii) using a simple "shim" protocol on top of IPv4 to extend addressing across IPv4 realms, localizing this extension to inter-realm gateways. We claim that TRIAD solves the problems with NAT, is incrementally deployable, and eliminates the need to make the painful transition to IPv6.