Jon,

The reamer follows the centroid of the hole, which has no guarantee of
being
anywhere near where you wanted the hole. So, better drilling techniques
will also give you a better final hole size. For almost any job where I
want
a hole to line up with something, I use a milling machine, clamp the
work in
a vise or to the table, and start the hole with a center drill first.
Once the
center drill has made a pretty good starting hole, the twist drill will
follow
with a lot less of this shuddering, and the final hole will be both more
round
and closer to where I started it. I usually get hole locations within a
few
thousandth of an inch of intended position this way. Using a center punch
and then drilling directly with a jobber's length drill, the hole
position can
drift 25 thousandths of an inch, or even more.

How much of a hole do you drill with the center? I've been following
Harold's recommendation to touch the work to make a mark and check the
location before doing further damageg - two fewer pieces of scrap and
counting. If where I intended, I enlarge the mark, but my gut sense
reading the above is that I should be doing more??

Bill