The drain in my shower is REAL slow. I tried using the standard drain
cleaning chemicals, but they didn't do much to improve it. I'd like
to auger or snake it out, but the opening is real small. Too small
for my drain auger.

I found a nice 1/8" SS Wire, pretty stiff, which I tried sticking down
the drain.

I found I can only get as far as the on/off plug. That is, the
vertical up and down shut-off that opens and closes the drain to allow
the tub to fill.

Any thoughts on the best way to clear such a small drain?