Rachford-Rice iterations are widely used in equation-of-state (EOS) flash calculations to determine phase equilibrium compositions from constant equilibrium ratios (K-values). The method, however, can be slow to converge or may not converge at all for cases where at least one overall composition is zero or negative. Having a robust method for flash calculations in these special cases is important in calculating the minimum miscibility pressure (MMP) using method of characteristics (MOC). This paper presents a simple, fast, and robust alternative to Rachford-Rice and similar methods in flash calculations, whether overall compositions are positive, zero, or negative. The new objective function has two fewer asymptotes compared to Rachford-Rice and is based on solving for one of the equilibrium phase mole fractions, typically the lightest component. Results with the new objective function demonstrate that rapid convergence using Newton-Raphson (NR) iterations is assured because the correct solution is determined within a small range (window). In that window, no poles exist no matter the overall composition and the objective function is often nearly linear. Improved linearity of the objective function contributes to increased convergence speed even near critical points. (C) 2011 Elsevier B.V. All rights reserved.