USB-->PS/2 converter

I have a cheap USB optical mouse which was plugged to my computer on the
PS/2 port with a converter which was included in the box. I also have a
puppy who got done with the converter, so I went and bought a couple of new
ones. They do not work with my mouse. I tested the mouse (plugging it USB)
and the port (plugging a PS/2 mouse) and everything worked. I tried another
converter from another computer, and doesn't work either.

Are those converters mouse-specific? Or what they have inside? I thought it
was just re-wiring. Can you think of any fixes?

Teilhard.