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Many radioisotopes with potential medical applications are difficult to produce routinely, especially those on the proton-rich side of the valley of stability. Current production methods typically use light-ion (protons or deuteron) reactions on materials of similar mass to the target radioisotope, which limits the elemental target material available and may require the use of targets with poor thermal properties (as is the case for the production of radiobromine). These reactions may also create significant amounts of proton-rich decay products which require chemical separation from the desired product in a highly radioactive environment. A promising alternative method using heavy-ion fusion-evaporation reactions for the production of the medically relevant bromine radioisotopes 76 Br (t 1/2  = 16.2 h) and 77 Br (t 1/2  = 57.0 h) is presented. Heavy-ion beams of 28 Si and 16 O were used to bombard natural chromium and copper targets just above the Coulomb barrier at the University of Notre Dame's Nuclear Science Laboratory to produce these bromine and precursor radioisotopes by fusion-evaporation reactions. Production yields for these reactions were measured and compared to PACE4 calculations. In addition to using more robust targets for irradiation, a simple physical-chemical separation method is proposed that will lead to very high radiopurity yields. A summary of accelerator facility requirements needed for routine production of these radioisotopes is also presented., (© 2021. The Author(s).)