Thanks Mark for the replies.  I wonder what's different about our installations?

I'd be happy with switching off the paddle, adjusting the pitch, and switching it back on -- that's my usual procedure with the 727 since the pitch/turn knob is such a pain to use.

I'll keep experimenting.  Did you replace the radios as suggested in another thread?  I did, had no effect on the problem.

Except for that problem the CS 737 is a fine old jet to fly.  I want to love it as much as I do the 727.  Having a few things quirky and broken is okay in old birds, except when it's something that affects your everyday flying.

UPDATE:  After extensive flight testing I have a procedure that works a treat.  Maybe it might help some others too.

I've been trying to adjust pitch using the yoke and/or trim buttons I have assigned to my joystick.  Not working reliably as I've said.

For grins I tried using the trim keys on my keyboard.  Perfection!  Using those the pitch trim can be adjusted reliably without the system fighting back.  It actually works like the pitch adjustment knob on the 727 only better.  I'm happy!

I have no explanation for why the keys would work and the joystick assigned buttons wouldn't.  (Joystick trim works great when autopilot is not switched on.) I thought, naively, that they were simply equivalent.  FS is such a quirky thing.  Learn something new every day.

Flipping off the elevator paddle still doesn't work: the airplane will try to hold nose attitude regardless of yoke input even with it off.  But with using the keyboard trim it doesn't matter anymore.

Dutch