Experimental criticality data do not exist for most plutonium compounds. To obtain guidelines for nuclear criticality safety use, a survey utilizing transport-theory calculations was made to determine the critical masses of bare and water-reflected spheres as a function of density and H:Pu ratio for 12 of these compounds in the undermoderated range (H:Pu ≤ 20). The compounds considered were: PuH2, PuH3, PuN, PuC, Pu2C3, PuO2, Pu2O3, PuF3, PuF4, PuCl3, Pu(NO3)4, Pu(C2O4)2. Also derived were core density exponents which permit critical masses to be predicted for compounds with densities ranging down to one-fifth of their theoretical values. The validity of the calculations was examined by comparing results with the limited criticality data on homogeneous PuO2 systems in the undermoderated range. Comparisons were also made for Pu metal systems and for three heterogeneous Pu-fueled assemblies.