Private phone numbers, I hate 'em!

The reason I hate private phone numbers is simple. I use the computer a lot during the day and the phone/fax is right next to me. I only have to pick up the handset on the first ring. This usually startles the caller, but it eliminates the confusion for them, as most people do not know if they have the right number when they hear the fax squeaking and screeching. Anybody who has a fax/phone will know to what I am referring. The machine has to decide if the call is a fax or a phone call. This only takes a few seconds but most people are too impatient to wait and hang up after the first ring.
I had a call just now, and picked the hand set up quickly, but not quickly enough. The caller had hung up in a split second, resulting in an unanswered call. When I dialed to see who it was, I was informed it was a private number. This number can not be returned. Bah, humbug!The other annoying thing about this situation is, they very seldom call back, and if I press one, to return the call, it is usually engaged, so I still never find out who called.