A library of 10 novel benzenesulfonamides containing triazole-tethered phenyl 'tail' moieties were synthesized by a Cu(I) catalyzed 1,3-dipolar cycloaddition reaction (DCR) (i.e., click chemistry) between 4-azido benzenesulfonamide and a panel of variously substituted phenyl acetylenes. These compounds were very effective inhibitors (low nanomolar) of the human mitochondrial carbonic anhydrase isozymes VA and VB. Mitochondrial carbonic anhydrases are potential targets for anti-obesity therapies, acting to reduce lipogenesis through a novel mechanism of action. The inhibitors reported here should prove valuable as lead compounds to further investigate the potential of CA inhibition for this novel therapeutic application.