The simplified-Pl(SPl) and modified-P2(MP2) transport approximations have been considered for use as practical nuclear design tools, replacing diffusion theory in the first few-group of a four-group scheme. Two numerical comparisons of two-dimensional systems indicate that SPl can be a satisfactory design tool for situations where the total cross section is slowly varying and the geometry is not too severe. The MP2 approximation has certain computing advantages, but does not yield as uniform an improvement over P1 as SPl does.