I used an imperial letter "A" drill, but the hole ended up a bit too big. Are there any other tricks that I'm missing?
RR
If you're trying to get a good fit out of your drill bits, they almost always cut oversized. Were that me trying to do this the hard way (You have good advice so far on the right way...). I keep a card with drill bit dimensions handy for dumb stuff like this. You're looking for 6mm, which is (about) 236 thousandths of an inch. A letter A at 235 thousandths is sure to be sloppy after it gets done oversizing the hole. The next two down, numbers 1 and 2 are 228 thousandths and 221 thousandths respectively. That's way too small, except all that is relative. "Way too small" in this case entails is eight or fifteen thousandths of an inch. a 0.228 drill bit that's cutting oversized (as it probably will) doesn't have to be out by much to be in the ballpark. I assume it's not "that" deep? Slip fit with a set screw? So drilled accuracy is fine? If you feel like playing with it, try drilling a test hole in a piece of similar material. Drill without oil. That tends to enlarge a hole "slightly". Or take one flute of a slightly undersized drill and just dust it ever so slightly on a fine stone to offset the point just a whisker. Not so much in the bigger sizes (although they can be adjusted), but in the smaller drills, with a bit of practice, you can really fill in the gaps if you put your mind to it. Assuming of course you need drilled hole accuracy. If you need better, reaming or boring is gonna be your best bet. It might or might not be a solution for this project, but it's a great thing to pay attention to, as every now and then it can bail you out of a pinch.