The most critical constraint on any model of the Snowball Earth is the source of alkalinity for the enigmatic carbonates that consistently cap Neoproterozoic glacial strata worldwide. In one end-member hypothesis the materials required for the caps are derived from the intense weathering of the continents under a CO₂-charged atmosphere. The distinct lack of clay, particularly kaolinite, and silica in cap lithofacies poses problems for this extreme view. Alternatively, carbonate alkalinity may have formed through 1) the dissolution of pre-existing carbonate, or 2) through bacterial sulfate reduction in sediments or the water column using methane or other low molecular weight organic compounds as terminal electron acceptors. Water column anoxia - similar to the present-day Black Sea - is supported by the observation that many of the glacial diamictites are cemented with iron oxides; high concentrations of both iron and manganese are also present in post-glacial carbonates. Sulfur isotope compositions of sulfides, barites, and structurally bound sulfate in cap carbonate lithofacies reveal extreme positive d³⁴S excursions. It is envisioned that during the ice age, bacterial sulfate reduction in deep anoxic oceans would have caused ³⁴S enrichment (and ¹³C depletion) in seawater as sulfide was removed as pyrite. In the aftermath, however, rising temperatures, dilution of sulfate-depleted seawater, and wind-driven upwelling likely resulted in the primary precipitation of cap dolostone. Continued ³⁴S enrichment in anachronistic cap lithofacies (as high as +50 permil) is modeled as a sedimentary phenomenon during extreme rates of carbonate accumulation (in excess of bacterial sulfate reduction), assuming that the glaciation lasted longer than the precipitation of the caps. The most striking result of the model calculations concerns a limit on the magnitude of the d³⁴S fractionation between oceanic sulfate and bacterially reduced sulfide, irrespective of the initial oceanic sulfur mass. The notable carbon isotope anomaly in the caps can also be explained through extreme rates of carbonate precipitation. In contrast, the sulfur isotope anomaly is inconsistent with a continental source of alkalinity, or with the alkalinity that may have been produced during a sudden release of methane into post-glacial seas.