Carbonic Anhydrases (CAs) are pharmaceutically relevant targets for the treatment of several disease conditions. The ubiquitous localization of these enzymes and the high homology shared by the different isoforms represent substantial impediments for the discovery of potential drugs devoid of off-target side effects. As a consequence, substantial efforts are still needed to allow for the full realization of the pharmacological potential of CA modulators. In this contribution, starting from our previous studies, we describe the synthesis of a set of new bicyclic tetrahydroindazoles featuring a secondary sulfonamide. Biological evaluation of the inhibitory activity against the hCA I, II, IV, and IX isoforms allowed drawing a structure-activity relationship profile that was rationalized through theoretical studies. This allowed dissecting the new molecules into the single portions influencing the zinc chelation properties and the selectivity profile thereby offering a new platform for the discovery of new isotype selective CA inhibitors.