A petty knife can be used for delicate tasks where a larger knife would get in the way. It is used to peel, shape, slice, and chop fruits and vegetables, as well as to chop herbs and make garnishes. The knife's small size and relatively narrow blade make it very maneuverable and suitable for making accurate cuts.
For boning tasks, there's the honesuki (for breaking down poultry) and hankotsu (for butchering hanging meat). Both of these knives can be used as general boning knives too.