Thanks all for your replies. Since they overlap a bit I'll respond to your suggestions collectively.
My Autosave is set to 5 minutes or 20 changes, 128 Undo levels. I believe that's the default.
Saves are only taking two or three seconds, but the dead time adds up. If it only happened every five minutes or so, I wouldn't care, but I'm having to wait after every split or trim.
I realize that this shouldn't happen if Autosave is turned off. But I don't particularly want to turn Autosave off. I am a non-recovering Ctrl-S addict, believe me, but it's nice to have Autosave as a backup; it's saved me more than once.
Why should my project be AutoSaving after every change when it's set to 5 minutes or 20 changes?