Herein we report the synthesis of two series of benzenesulfonamide containing compounds that incorporate the phenyl-1,2,3-triazole moieties. We explored the insertion of appropriate linkers, such as ether, thioether, and amino type, into the inner section of the molecules with the intent to confer additional flexibility. All obtained compounds were screened in vitro as inhibitors of the physiologically relevant human (h) isoforms of the metalloenzyme carbonic anhydrase (CA, EC 4.2.1.1). Many of them were low nanomolar or subnanomolar hCA II, IX, and XII inhibitors, whereas they did not potently inhibit hCA I. Computational and X-ray crystallographic studies of the enzyme-inhibitor adducts helped us to rationalize the obtained results. Some of the sulfonamides reported here showed significant intraocular pressure lowering activity in an animal model of glaucoma.