I think this is a newbie question with an easy answer -- at least I hope it is. I need to drill a coaxial hole into the end of a 1 1/4 inch dowel. I can get it centered, but I'm having trouble getting it straight. What I've tried a few times is clamping the dowel in a vice and using a small level to make sure it's vertical. Then I use the bubble in my cordless drill to drill the hole straight down -- or at least that's what I try to do. I'm getting close to straight, but not close enough. Is there a better way to do this (without a drill press, which I don't have)? Are there any (inexpesive) jigs made for this sort of thing?

P.S. I thought I posted a similar message earlier today, but I don't see it anywhere. So I must have done something wrong.