To express myself a bit more fully, separating out asexuality on account of people's varying preferences within the umbrella strikes me as no different from separating out pan/bisexuality because some people tend more towards their own gender and others tend towards the opposite, or indeed have only had experience one way or another. Everyone's sexual identity is more complicated than a simple label, but those complications don't affect the accuracy of 'asexual' as a description any more than in the case of other identities. I think what I'm basically saying is that being asexual doesn't co-exist with another identity, or act as a qualification of it, because it's far more central than that. Being a 'straight asexual' is nowhere near the same as being straight, though people might not notice the difference to start with, while a 'straight asexual' and a 'gay asexual' will most likely have very similar experiences.