<< I've got the Mouseman wheel optical, and the original Mouseman Wheel with the ball.
Funny thing, in WinME the Mouseman optical doesn't do well if you move it really fast, like when going from one side of the screen to the other with the curser as fast as you can. It just stutters and the cuser stays where it is. It doesn't do that in Win2K though.
Otherwise it's a great mouse, although I think they made the thumb button too hard to push. I like how easy it was to push on the old Mouseman ball.
So I still use my original Logitech Mouseman for games. >>
I have the mouse, but not using WinME, so can't test, but if you are using the PS/2 adapter on it then the problem might be sampling rate. I think the sampling rate in win9X is either 30 or 40 times per second. NT/2000 defaults to 60/sec for PS/2. You can change this with PS2Rate for win9X or in the device manager advanced properties for the mouse in 2000 (up to 200Hz, I think). If you use the USB connection then the sampling rate is 120Hz in both 9X and NT/2000, I believe.