Thanks everyone! Dionysus, I'm sure I'll see you around, but I probably won't know who you are, nor you me ;).
Stats, as requested:
GRE: 800 800 6.0
CS GRE: 830 (87%)
GPA: ~3.98
MAJORS: CS & Math
RESEARCH: 2 Projects, no papers
SCHOOL: Small liberal arts college, but has sent a few grads to Columbia's CS PhD before.
FELLOWSHIPS: Won 2, actually, and an Honorable Mention for a third, but I only told Columbia about one of them (other's came after I was accepted) so I don't think they count. I'm taking only one, of course.
OTHER: I took a course in Columbia last semester with the professor who admitted me into his lab, which was certainly helpful. I basically haunted the CS department for a few months, visting a bunch of professors and trying to keep my name on their minds.