An extremely simple iterative procedure is described for performing group-diffusion calculations in two and three dimensions No proofs have been found to guarantee its convergence, but successful experience with a wide variety of problems, some realistic, others with specially introduced difficulties, shows the method to be rapid and reliable. Three large computer programs have been devised embodying the principle: EQUIPOISE-3, TWENTY GRAND, and WHIRLAWAY. The first two are two-dimensional programs, while the third is three-dimensional. If desired, the programs can be used to compute adjoint fluxes and those integrals necessary for perturbation calculations automatically. Possible further applications of the method are suggested.