The relationship between ∆36S and ∆33S in Archean sedimentary pyrites has been used to evaluate early geologic processes, including photochemical reactions in the anoxic atmosphere, biological activity and thermochemical alteration during sediment deposition. We have applied statistical methods to quadruple S isotope analyses of Archean sedimentary pyrites, using data compiled from the literature. Most of the best-fit lines, on plots of ∆36S against ∆33S, have Archean reference array-like ∆36S/∆33S slopes that vary between −1.5 and − 0.9. Rigorous statistical tests were conducted to calculate the probability of the best-fit lines passing through the origin. Seventeen of 23 ∆36S-∆33S regression lines, which pass our reliability filter of R2 ≥ 75% and ∆33S range ≥ 2‰, have positive intercepts on the ∆36S axis, and 13 of these have a probability of < 5% of a zero intercept on the ∆36S axis. The observed ∆36S/∆33S slopes and the non-negative intercepts, which requires at least two mass-independent fractionation source reactions to operate simultaneously, can be produced by UV radiation in the atmosphere at low SO2 partial pressures by combining collision-induced intersystem crossing in the SO2 photoexcitation band (240–340 nm), with the self-shielding effect in the SO2 photolysis band (190–220 nm). The two SO2 photochemical processes must occur simultaneously in a single atmospheric reservoir in order that the fraction contributed by the end-member process remains constant across the full range of ∆33S values. We call this process simultaneous fractionation. We applied a two-end-member model to calculate the fraction of S contributed by the SO2 photoexcitation end-member (f) needed to produce the observed ∆36S/∆33S gradients and variable intercepts on the ∆36S axis in the Archean sedimentary pyrites, when the other end-member is SO2 photolysis with the self-shielding. The simplest explanation for variations in f, and therefore variations in ∆36S/∆36S gradients, is that it is controlled by changes in the partial pressure of SO2 in the atmosphere.