We extend the phase space slicing method of Giele, Glover and Kosower for p
erforming next-to-leading order jet cross section calculations in two impor
tant ways: we show how to include fragmentation functions and how to includ
e massive particles. These extensions allow the application of this method
not just to jet cross sections but also to cross sections in which a partic
ular final state particle, including a D or B meson, is tagged. [S0556-2821
(99)00611-6].