This makes the most sense so far, as the mouse I am having trouble with did *not* originally come with a PS/2 adapter. It is marketed as a 'USB mouse' only.
I must correct what I said previously also. Not *all* of my optical mice cease to function with the Cocolino. As it turns out, the Microsoft Optical Wheel mouse is working fine! I somehow lumped it in with the Logitech as having trouble as well. I was so pleased to discover the the MS Optical was working, I went out and picked up a black colored one to match my keyboard, monitor, etc. My original "Wheel Mouse Optical" was white.

And to answer the other suggestion that power may be involved-- both my working Wheel Mouse Optical and the non-working Logitech optical are rated at "5V, 100mA". Incidentally, I am using the Cocolino with an A3000 desktop.
That is interesting about the "modes" making the difference in this case.
Thomas wrote:
Every PS/2 mouse should work with the Cocolino, optical or not.
The matter with USB/PS2 adapters is the same as with PS2/serial adapters: the mouse has to support both modes. An USB-only mouse does not work with an USB/PS2 adapter of another mouse. Usually a mouse which did not come with an adapter does not work with an adapter.
I have two Logitech optical mice (one cordless and one with a long tail) and both work without problems. As do cordless and non-cordless mice with a ball. I didn't yet find a mouse which didn't work.
Bye,
Thomas