A computer system maps unique addresses to the conventional fax numbers of conventional fax devices (such as conventional fax machines and computing devices having conventional fax capabilities). A transmitting user who is connected to the Internet may send an IP fax to a receiving user who is also connected to the Internet by addressing the receiving user using the receiving user's unique address, even if the sending user and receiving user are not within the same local network. A server outside of the receiving user's local network mediates the transmission of the IP fax from the transmitting user to the receiving user. The server may select a preferred transmission method of the recipient (e.g., conventional fax, IP fax, email, or secure document delivery) and transmit the fax to the receiving user using that preferred transmission method. Transmitted faxes may be in color and/or contain high-definition content.