Here's a note of caution for you. I think most of you may have the original tubs with the triangular shaped overflow drain cover with the lever fill-or-drain the tub. Turns out on my tub, the mechanism attached to the lever had corroded and fallen into the drain pipe. This is causing the tub to not drain properly.
I recommend that you open the overflow drain cover and remove that fill-drain assembly. Before it corrodes. And then use a rubber stopper. I understand from the plumber that this corrosion happens a lot.
The problem is that if that assembly falls in and you can't fish it out with a coat hanger, then the only option is to open up the floor. Or live with a slow/non draining tub (arg!!!)
I'm still fishing... If anyone has successfully done this before, let me know if you have any tips!