Cached or predictive negotiation of compression parameters over a modem relay network connection involves method and apparatus for determining at a gateway the identity of a client/server modem that is called or calling, and using a profile of such called or calling client/server modem, the profile being stored at the gateway or an affiliated agent, to transmit respectively a candidate response or command containing compression parameters. Preferably, a candidate response or command includes an exchange identification (XID) or link request (LR) command or response, either provisioned, i.e. manually configured or automated, i.e. computer-generated. The profile is stored in a memory. The actual achieved parameters for a given call also may be stored, e.g dynamic learning may be had. Finally, establishing such profiles by placing dummy calls once the modem's phone number is known also is described as a feature of the invention.