Never undercut the inked area!
You might want to experiment with some other carving tools, such
as a Speedball cutter,or a set of woodcarver's knives. These can
be especially useful in carving out and leveling off the valleys
between the inked ridges.
nice tool is a sewing needle with its head pushed into the end of
a wooden handle. This can be used to prick out very intricate details.
When you have finished the carving, press it onto an inked pad and
try it out on a piece of paper.
may want to make a few touch-up cuts here and there once you've
inspected your test prints.
you're happy with the results, cut away the excess material around
the edges of your design.