Dats cuz yer brand new chinese/craftsman drill press comes w/ a brand new
crappy chuck.
Yeah - I can't stand that spring loaded thingee in it.

I know, cuz I got one. Like Grant sez, you must tighten from all three
holes.
I wasn't doing that so it will be my first thing to try tomorrow. Newbies +
power tools = please stand back! :-)

They make sets of drills w/ hex shanks, which fit into electric
screwdrivers, etc. Really handy, actually, and will partially solve this
problem--at a price. HD has them.

You could also grind flats on your drills. The better you grind them, the
more concentric your drill will remain. Tough to do accurately by hand,
simple on a surface grinder w/ a spin fixture.

That spin fixture sounds like a neat trick. Never heard of it before but I
think I get the idea. I'll Google it.

Thanks again for the tips!
JCD