Boron neutron capture synovectomy is a novel approach for the treatment of rheumatoid arthritis. The goal of the treatment is the ablation of diseased synovial membranes in articulating joints. The treatment of knee joints is the focus of this work. A method was developed, as discussed previously, to predict the dose distribution in a knee joint from any neutron and photon beam spectra incident on the knee. This method is validated and used to design moderators for the deuterium-deuterium (D-D) and deuterium-tritium (D-T) neutron sources. Treatment times >2 h were obtained with the D-D reaction. They could potentially be reduced if the 10B concentration in the synovium was increased. For D-T neutrons, high therapeutic ratios and treatment times <5 min were obtained for neutron yields of 1014 s-1. This treatment time makes the D-T reaction attractive for boron neutron capture synovectomy.