Trypanosoma cruzi, the causative agent of Chagas disease, encodes for an α-carbonic anhydrase (CA, EC 4.2.1.1) possessing high catalytic activity (TcCA) which was recently characterized (Pan et al. J. Med. Chem. 2013, 56, 1761-1771). A new class of sulfonamides possessing low nanomolar/subnanomolar TcCA inhibitory activity is described here. Aromatic/heterocyclic sulfonamides incorporating halogeno/methoxyphenacetamido tails inhibited TcCA with KIs in the range of 0.5-12.5 nM, being less effective against the human off-target isoforms hCA I and II. A homology model of TcCA helped us to rationalize the excellent inhibition profile of these compounds against the protozoan enzyme, a putative new antitrypanosoma drug target. These compounds were ineffective antitrypanosomal agents in vivo due to penetrability problems of these highly polar molecules that possess sulfonamide moieties.