Yes. I use BitBucket because it allows free private repositories. No problems at all.

I like Unfuddle. I'd put more stuff there, but nobody would see it if I did. For many people it's like if code isn't on GitHub it doesn't exist.

He doesn't even have to use bitbucket, it sounds like he can just create another github project. I think he's not asking for alternatives though, just explaining the situation and calling attention to it.

PS

I am also a bug fan of bitbucket, I got three groups on it, using it unlimited mode, since they are research/education related (emails).

I use BitBucket for private repos and GitHub for public-facing resume stuff. Generally works best.