In the design of nuclear reactors it is frequently necessary to adjust the parameters appearing in the equations describing neutron transport, e.g., the macroscopic absorption cross section in the diffusion equation, in order to force region reaction rates to agree with results of more exact calculations or experiment. Given a multiregion cell problem with a specified absorption rate in each region it is proved that there exists, for any neutron transport equation that has a solution that is everywhere positive, a non-unique set of region absorption cross sections which yield the specified absorption rates; however, if the cross section is fixed in one region, the set is, in a specially defined sense, unique. Two systematic iterative methods for obtaining such sets of region cross sections are presented; one of these methods has been incorporated into a computer program.