The effect of precipitation of mineral phases on the sulfur isotopic composition of hydrothermal minerals is quantitalively evaluated in terms of a Rayleigh distillation process. The precipitation of either sulfate or sulfide minerals is considered as the removal mechanism for dissolved sulfur from a finite solution reservoir. The isotopic composition of sulfur in hydrothermal minerals is strongly controlled by the fraction of sulfur remaining in the solution as well as by the relative proportions of oxidized to reduced sulfur compounds. When sulfate is precipitated from a SO42--dominant solution with minor amounts of H2S, its deltaS-34-value can change, with time, from slightly greater than that of the original solution in early stages to significantly lower than that of the original solution in late stages. Conversely, when sulfide minerals are deposited from a H2S-dominant solution with minor amounts of SO42- their deltaS-34-values may resemble the deltaS-34-value of the original solution in early stages, but may change to values remarkably higher than that of the original solution in late stages. Sulfur and oxygen isotopic data for barite from the Bad Grund Pb-Zn deposit in the Harz Mountains, Germany, illustrate the application of the reservoir effect, and a few barites with low deltaS-34-values are interpreted to represent the product of precipitation of the gangue mineral in late stages.