Q: Back up and restoring ringtones

Yes, the above responses helped.  The steps I suggest would be to (1) open iTunes, (2) connect your iPhone, but CANCEL the syncing, which will otherwise overwrite your phone contents with the iTunes library info, which doesn't include the ringtones [This is done either by hitting the cancel "x" in the sync window or holding the COMMAND and OPTION keys (Apple) or the CONTROL and SHIFT keys (PC) when opening iTunes.], (3) selecting backup to the computer, which backs up the phone content, including the ringtones, to the computer.  THEN, after making your sync selections include ringtones (and anything else you want to move onto the phone from iTunes), you can then, or when you choose, sync the chosen iTunes content onto the phone.  (This will be done automatically when the phone is connected and the syncing is not canceled as described above.  WHEW.