Carbonic anhydrases (CAs, EC 4.2.1.1) are ubiquitous isozymes involved in crucial physiological and pathological events, representing the targets of inhibitors with several therapeutic applications. In this connection, we report a new class of carbonic anhydrase inhibitors, based on the thiopyrano-fused pyrazole scaffold to which a pendant 4-sulfamoylphenyl moiety was attached. The new sulfonamides 3a−e were designed as constrained analogues of celecoxib and valdecoxib. The most interesting feature of sulfonamides 3 was their predominantly strong inhibition of human (h) CA I and II, as well as those of the mycobacterial β-class enzymes (Rv1284, Rv3273, and Rv3588c), whereas their inhibitory action against hCA III, IV, VA, VB, VI, VII, IX, XII, XIII, and XIV was found to be at least 2 orders of magnitude lower. X-ray crystallography and structural superposition studies made it possible to explain the very distinct inhibition profile of the tricyclic sulfonamides, different from those of celecoxib and valdecoxib.