I'm sorry -- you said brew the tea in the pot you heated the water in?

Do you mean I should boil the water and then infuse the leaves in some
sort of pan? I use a kettle, like most people, to heat the water. The
two-pot method I know about boils the water in a kettle, pours over the
leaves in the brewing pot, then strains the liquid (immediately once
it's done) into the serving pot. I don't mind needing two pots, it's
all the fussing about making sure that both are warmed and such that
would start to grate on the nerves.

You're right about infuser baskets being a compromise. But given what
has been discussed here so far, I think I will use my basket when I'm
brewing Assam (and posibly Darjeeling), but not for some of the
larger-leafed Chinese blacks and certainly not for most greens. It
turns out to not be that much of a hassle to clean out the pot anyway
-- I've made a special straining contraption out of a large yogurt
container with holes cut into the bottom with an exacto knife.

I just dump the leaves after a few rinses into that container which
fits perfectly over my sink hole -- I leave it there, and in about ten
minutes the water has drained off. If I had one of those fancy sinks
with a garbage disposal unit built-in, I wouldn't have to do that.