Transmutation of the radiotoxic isotopes 137Cs and 129I using a muon-catalyzed fusion (CF) neutron source is considered. Extensive Monte Carlo simulations show that each fusion neutron may transmute up to 1.7 radiotoxic nuclei, depending on geometry and choice of material. Further, it is found that chemically confining cesium atoms in the compound Cs2O leads to higher transmutation efficiency for a given volume as compared with pure cesium. Assuming that a minimal requirement for applying transmutation to 137Cs is that the inventory half-life with respect to undergoing transmutation is less than twice the natural half-life T1/2 = 30 yr, the highest transmutation rate in a system consisting of a CF source with a maximum achievable intensity of 5 × 1018 n/s is ~5 kg/yr, at an inventory of 300 kg. For larger inventories, the half-life becomes longer. Hence, it seems difficult to achieve a positive energy balance in the process, in contradiction with results of a previous study.