I've looked for responses on this subject that parallel my experience,
but I saw none.  I use a hand cleaner containing lanoline intended for
use by mechanics.  Use the type without the lava or pumice. It comes in
round containers and I use a medium bristle brush (toothbrush for
carvings or smaller surfaces) to apply it and stroke it around until
the dirt no longer comes off the surface.  Soft paper towels may be
used to swirl it around and more towels are used to clean the surface.
If refinishing is intended, the surface must be cleaned free of any
traces of this cleaner.  I use Mohawk dewaxer for this, but other
dewaxers or degreasers will probably work as well. If you choose the
right hand cleaner you will end up with a very pleasant odor on your
freshly cleaned surface.

Bill Maier (Scottsdale AZ and Sandy UT)