The efficacy of the overlapping group method in fast-reactor analysis is investigated and tested on an idealized fast-reactor configuration. A full transport-theory treatment is adopted and the overlapping group equations are derived by the indirect use of a variational principle. A number of refinements to the basic method have been examined and serve to demonstrate that with a judicious choice of variational functional and trial functions it is possible to obtain accurate estimates not only of the reactivity and other integral quantities but also of the detailed flux. These include: leaving both the space/angle and energy dependence of the trial functions to be determined by the variational principle, incorporating discontinuous trial functions, and the use of a new variational principle for criticality problems that leads to estimates of homogeneous functionals of the unknown flux.