Three distinct series of isoxazole-based primary mono- and bis-sulfonamides have been synthesized via direct sulfochlorination, each of them delivering nanomolar inhibitors of human carbonic anhydrase. Certain pronounced SAR trends have been established and rationalized by in silico docking. These findings expand the structure-activity knowledge base for heterocycle-containing sulfonamide carbonic anhydrase inhibitors and further validate the power of direct electrophilic sulfochlorination as a means of introducing the pharmacophoric primary sulfonamide group into structurally diverse aromatic precursors.