Minor sulfur isotope anomalies indicate the absence of O2 from the Archean atmosphere. A rich dataset showing large variations in magnitude and sign of Δ33S and Δ36S, preserved in both sulfates and sulfides, suggests that further constraints on Archean atmospheric chemistry are possible. We review previous quantitative constraints on atmospheric Δ33S production, and suggest that a new approach is needed. We added sulfur species containing 33S and 34S to a 1-D photochemical model and describe the numerical methodology needed to ensure accurate prediction of the magnitude and sign of Δ33S produced by and deposited from the Archean atmosphere. This methodology can test multiple MIF-S formation mechanisms subject to a variety of proposed atmospheric compositions, yielding Δ33S predictions that can be compared to the rock record. We systematically test SO2 isotopologue absorption effects in SO2 photolysis (Danielache et al., 2008), one of the primary proposed mechanisms for Δ33S formation. We find that differential absorption through the Danielache et al. (2008) cross sections is capable of altering predicted Δ33S as a function of multiple atmospheric variables, including trace O2 concentration, total sulfur flux, CO2 content, and the presence of hydrocarbons, but find a limited role for OCS and H2S. Under all realistic conditions, the Danielache et al. (2008) cross sections yield Δ33S predictions at odds with the geologic record, implying that additional pathways for sulfur MIF formation exist and/or the cross sections have significant errors. The methodology presented here will allow for quantitative constraints on the Archean atmosphere beyond the absence of O2, as soon as additional experimental measurements of MIF-S producing processes become available.