An intelligent FAX machine monitors a shared telephone line after another telephone has taken it off-hook. If preliminary signals from a sending FAX machine to another telephone on the same line are detected, then the FAX machine also goes off-hook and tries to establish a link with the sending FAX machine. Presumably the other telephone will hang up. E.g., a telephone answering device (TAD) automatically detects a parallel set going off-hook, causing the TAD to go on-hook. If the parallel telephone is an ordinary telephone, then that user may merely hang up after hearing FAX signals. In another aspect, the FAX machine picks up incoming calls from known FAX machines before a second ring (or before a third ring), based on Caller ID information, so that other pre-configured ring-count telephonic devices such as a telephone answering machine can be operated in an automatic mode with a higher pre-configured ring count.