The behaviour of sulfur in magmas is complex because it dissolves as both sulfide (S2-) and sulfate (S6+) in silicate melt. An interesting aspect in the behaviour of sulfur is the solubility minima (SSmin) and maxima (SSmax) with varying oxygen fugacity (fO2). We use a simple ternary model (silicate–S2–O2) to explore the varying fO2 paths where these phenomena occur. Both SSmin and SSmax occur when S2- and S6+ are present in the silicate melt in similar quantities due to the differing solubility mechanism of these species. At constant T, a minimum in dissolved total S content (wmST) in vapour-saturated silicate melt occurs along paths of increasing fO2 and either constant fS2 or P; for paths on which wmST is held constant with increasing fO2, the SSmin is expressed as a maximum in P. However, the SSmin is not encountered during closed-system depressurisation in the simple system we modelled. The SSmax occurs when the silicate melt is multiply-saturated with vapour, sulfide melt, and anhydrite. The SSmin and SSmax influence processes throughout the magmatic system, such as mantle melting, magma mixing and degassing, and SO2 emissions; and calculations of the pressures of vapour-saturation, fO2, and SO2 emissions using melt inclusions.