If you have a "good" knife and it has a double grind (eg. either a flat grind with an edge grind or a hollow grind with an edge grind) I would not have it ground to a zero bevel grind. A knife should really be planned to have a zero bevel grind, not altered later to have one. Zero bevel ground knives are not actually "sharper" than a double ground knife. The only way to make it sharper per se is specifically to decrease the angle of the edge grind (whether this is done through a zero degree grind or a double grind with a shallow edge grind angle is irrelevant). It is always a compromise when grinding an edge to a more shallow angle. The compromise is between edge strength and the sharpness of the edge. Scalpels are normally ground with a 10 degree edge, however, that edge will not hold up to a hard material such as wood. A 30 degree edge grind will hold up to wood, however it will not be as sharp as a scalpel edge ground to 10 degrees. One other thing to take into account is that you can actually shave with an edge ground at 30 degrees if that edge is finely honed or stropped.
--Wintermute