NOTE, ADDED 2/13/15: See next post for more discussion of carving thin lines.
There was a discussion a week or two ago on the Facebook page of the Baren Forum (a group dedicated to watercolor woodblock printing) about carving fine lines on shina plywood, so I wanted to address this post to that topic. Many woodblock artists insist that a fine keyblock can't be cut on shina (a Japanese wood related to bass wood or linden) and must be cut on a harder wood like maple or cherry. The Japanese ukiyo-e masters used cherry. However, I've found that for my purposes shina is OK for fine lines. I use a Japanese knife tool called a hangi-to, which resembles an X-Acto blade, to cut on either side of the line work. Then I clear around the knife lines with gouges.
Below is the key block for my "A Real Fake" print with the paper hanshita (sketch) removed. Now I'll go back in with my knife and touch up the lines to make some of them thinner still.
For more info on cutting lines, see this blog post.