The technique of boron neutron capture therapy in the treatment of cerebral gliomas depends upon the selective loading of the tumor with a 10B-enriched compound and subsequent irradiation of the brain with low-energy neutrons. The charged particles produced in the 10B (n,alpha) 7Li reaction have ranges in tissue of less than 10 mum so that the dose distribution closely follows the 10B distribution even to the cellular level. The effectiveness of this therapy procedure is dependent not only on the 10B compound but on the spectral characteristics of the neutron source as well. Hence, an optimization of these characteristics will increase the chances of therapeutic success. Transport calculations using a neutral particle transport code have been made to determine the dose-depth distributions within a simple head phantom for five different incident neutron beams. Comparison of these beams to determine their relative therapeutic efficacy was made by the use of a maximum useable depth criterion. In particular, with presently available compounds, the MIT reactor (MITR) therapy beam (a) is not inferior to a pure thermal neutron beam, (b) would be marginally improved if its gamma-ray contamination were eliminated, (c) is superior to a partially 10B-filtered MITR beam, and (d) produces a maximum useable depth which is strongly dependent upon the tumor-to-blood ratio of 10B concentrations and weakly dependent upon the absolute 10B concentration in tumor. A pure epithermal neutron beam with a mean energy of 37 eV is shown to have close to the optimal characteristics for boron neutron capture therapy. Futhermore, these optimal characteristics can be approximated by a judiciously D2O moderated and 10B-filtered 252Cf neutron source. This tailored 252Cf source would have at least a 1.5 cm greater maximum useable depth than the MITR therapy beam for realistic 10B concentrations. However, at least one gram of 252Cf would be needed to make this a practical therapy source. If the moderated 252Cf source is not 10B filtered, the resultant neutron beam has characteristics similar to those of the MITR beam with no gamma-ray contamination. For usch a beam, 100 mg of 252Cf would produce a flux of 2.4 X 10(8) neutrons/(cm2 sec), which is an intensity suitable for therapy applications.