The so-called "sugar approach" in the field of human Carbonic Anhydrase (hCA) inhibition is the installation of a hydrophilic sugar moiety in the tail of a sulfonamide derivative to induce selectivity towards the different isoforms. Further investigations on our related "azasugar approach" variant, where the sugar is replaced by a polyhydroxypiperidine with a basic nitrogen atom, are reported. The synthesis and biological evaluation of a series of benzenesulfonamides, urea-, thiourea-, or amide-analogues of previously assessed inhibitors but lacking the triazole ring in the connecting chain to the azasugar, has allowed to draw some hints, albeit the precise effects on inhibition of a given hCA isoform needs to be evaluated case by case. The "triazole" benzenesulfonamide azasugars showed a general increase of selectivity in inhibition of the tumor-associated hCA XII with respect to other isoforms when compared to the corresponding "non-triazole" inhibitors and a triazole thiourea resulted two order of magnitude more active than towards cytosolic hCA II. The new "non-triazole" benzenesulfonamide azasugars resulted less selective but very good inhibitors of other clinically relevant hCA isoforms. Three "non-triazole" thiourea derivatives resulted better inhibitors of the transmembrane isoform hCA IX, related to tumor progression, than the reference acetazolamide, with Kis in the low nanomolar range. Molecular docking analyses of a few selected "triazole"/"non-triazole" couples of inhibitors towards the tumor-associated hCA isoforms were carried out in order to highlight the possible origin of the different inhibitory profiles.