This is the ASCII-art drawing I said I was going to post. (Sorry about
the HTML formatting--it's done to make sure that the drawing is shown in
fixed width font.)

------------ --- shower drain strainer
| | --- small tabs bent to point downward

___ ___
'--... ...--'
||| ||| --- Middle ring: black rubber?/plastic? gasket? (depth unknown)
| | | | --- Outer ring: PVC shower drain
| |
| | --- Inner ring: PVC drain pipe
| |

Note: tops of drain pipe and gasket? too high, interfering with
the "tabs" on the strainer