A series of polycyclic imides was prepared by reaction of the benzenesulfonamide with an appropriate polycyclic acid anhydride in refluxing glacial acetic acid. The synthesized mono- and bis-sulfonamides were evaluated as a carbonic anhydrase inhibitors (CA, EC 4.2.1.1), more precisely against the human (h) isoforms hCA I, II, IX and XII, some of which are involved in various pathologies, such as glaucoma, epilepsy and cancer. Several low nanomolar and isoform-selective hCA II, IX and XII inhibitors were detected, and the structure-activity relationship for CA inhibition with this class of compounds is discussed in details. Computational studies allowed us to explain the efficacy and isoform-selective behaviour for some of these enzyme inhiibtors.