A detailed study is reported of the influence of protons, metal cations, and media on the redox chemistry of lacunary anions [alpha-SiW11O39]8- and [alpha-PW11O39]7- of high formal negative charge. Each anion displayed a single chemically reversible one-electron reduction process in carefully dried aprotic CH3CN solution. This process was detected at very negative potentials just prior to the solvent limit. Addition of 0.3 equiv of acid gave rise to a new reduction process at considerably less negative potentials, which is attributed to formation of the protonated species [SiW11O38(OH)]7- and [PW11O38(OH)]6-. Voltammograms derived from simulations based on a double-square scheme are in excellent agreement with experiment. Previous data reported the presence of several processes in CH3CN and appear to have been influenced by the presence of protons and/or adventitious water. Not surprisingly, protonation reactions coupled to charge transfer contribute significantly to the voltammetry of these lacunary anions in buffered aqueous media over the pH range 2-6. A multi-square-scheme mechanism allowed the essential thermodynamic and kinetic features of this system to be captured and an assessment of the relative significance of possible individual pathways. The high formal anionic charges of [SiW11O39]8- and [PW11O39]7- appear to provide highly basic reduced forms that are able to abstract protons from water to produce protonated species which are reduced at potentials more than a volt less negative than those for the processes [SiW11O39]8-/9- and [PW11O39]7-/8- found in dry aprotic media.