A series of novel benzene- and 2,3,5,6-tetrafluorobenzenesulfonamide was synthesized by using a click chemistry approach starting from azido-substituted sulfonamides and alkynes, incorporating aryl, alkyl, cycloalkyl, and amino-/hydroxy-/halogenoalkyl moieties. The new compounds were medium potency inhibitors of the cytosolic carbonic anhydrase (CA, EC 4.2.1.1) isoforms I and II and low nanomolar/subnanomolar inhibitors of the tumor-associated hCA IX and XII isoforms. The X-ray crystal structure of two such sulfonamides in adduct with hCA II allowed us to understand the factors governing inhibitory power.