I really like the idea of more obscure covers. Our music is definately not top 40 stuff so I don't want to go there with covers. Also, there are so many songs on so many albums that never made the radio (or very little radio) that is really good.We'd do obscure or at least lesser known stuff, that fans may have been familiar with, but not so popular in general (example: we'd play The Beatles, She said She said...but not Come Together). Basically, we shied away from 'hit' songs or anything that most of the dedicated covers bands were likely to include in a set list.
This way you can play with them a little and put your own spin on them so that they don't sound completely out of place in your set list. That was our take on it at the time anyway, whether is was right or wrong is not for me to say. It seemed to work well though.
I just think that, in general, when people see a band they want some familiarity in what they are listening too.