Using Gibbs-Duhem integration and semigrand canonical Monte Carlo simulations, temperature vs. composition phase diagrams for a binary Lennard-Jones mixture, sigma(11)/ sigma(22) = 0.85 and is an element of(11)/is an element of(22) = 1.6, are calculated at several reduced pressures in order to examine the effects of pressure on complete phase behavior (that is, equilibrium between vapor, liquid, and solid phases). Interference is observed between the vapor-liquid and solid-liquid coexistence regions at the lowest pressure. As the pressure increases, the vapor-liquid coexistence region shifts to higher temperatures, while the solid-liquid coexistence region remains essentially unaffected. Eventually, the vapor-liquid coexistence region lifts off the solid-liquid coexistence region, ending the interference. Pressure vs. temperature projections for binary Lennard-Jones mixtures at sigma(11)/sigma(22) = 0.85, 0.9, and 0.95, and is an element of(11)/is an element of(22) = 0.45 and 1.6 are also presented to explore how the three-phase loci (solid-liquid-vapor and solid-solid-liquid) change with variations in diameter ratio and well-depth ratio. It is found that as the diameter ratio decreases, the maximum pressure in the solid-liquid-vapor locus decreases and the characteristic shape of the solid-liquid coexistence region changes from peritectic to eutectic. As the well-depth ratio decreases, the maximum pressure in the solid-liquid-vapor locus increases. For one mixture, sigma(11)/sigma(22) = 0.9 and is an element of(11)/is an element of(22) = 1.6, a quadruple point of solid-solid-liquid-vapor coexistence is located. (C) 2004 American Institute of Chemical Engineers