Is it possible to make 'anisotropic' cloth?

I love using cloth physics, which I use to create static geometry (that I deform with bones as necessary.)

One of the issues I run into when using cloth physics is that all of the parameters are vertex properties, rather than, I dunno, edge properties, if such a thing exists. For example, sometimes I want to make a t-shirt with a lot of shrink along the horizontal threads, but not a lot of shrink along the vertical threads. Or I want to make something like a belt, which has a very high structural value in one axis (it doesn’t flop on its twist axis) but not in the other axis (it rolls up easily).

I haven’t had good luck with subdividing manually and removing alternate loops-- it tends to look chunky, it’s tedious, and it doesn’t support further pre-physics subdivision.

Are there any tricks to making cloth physics behave like this?