My computer is in a different room from where the phone jack is. So, I have a splitter on the phone jack, with one line going to the phone, and the other longer line going to the room with the computer. At the end of this longer line, I split it into two, with one going to the 56K modem, and the other going to the OvisLink ethernet modem. If instead I put a three-way splitter at the jack, and had one line go to the phone, with the other two go to the computer, do you think this would work? Is this sort of what you were suggesting? I'll give this a try.
The only reason it's a concern is that I'll be running a webserver. So, I'd prefer to not worry about it disconnecting every time there's a fax. I'm getting an additional number with a different ring on the same line, and for the fax I'll filter out regular calls with a "ring selector