Processes and systems for transferring communication messages, such as fax and voice messages, between a computer and a terminal are disclosed. For example, a fax message intended for a user is received at a call processing system. A voice message intended for the user is received at the call processing system. An initial portion of the fax message and the voice message are transferred to a user terminal. The user can view the initial portion of the fax message and listed in the initial portion of the voice message using the user terminal. At least a second portion of the fax message is downloaded to the user terminal in a trickle mode, and at least a second portion of the voice message is downloaded to the user terminal in a trickle mode.