Cubic equations of state (EoS) are often used for correlating and predicting phase equilibria. Before extending any EoS to mixtures, reliable vapor-pressure prediction is essential. This requires experimental, if possible, critical temperatures T-c, pressures P-c, and acentric factor omega or extensive pure-compound vapor-pressure data which, for heavy and/or complex compounds, are often not available. This work presents a method for estimating T-c, P-c, and omega values for heavy compounds (typically with MW > 130) suitable for vapor-pressure calculations with generalized cubic EoS. The proposed scheme employs a recent group-contribution method (Constantinou et al. Fluid Phase Equilib. 1995, 103 (1), 11) for estimating the acentric factor. The two critical properties are estimated via a generalized correlation for the ratio T-c/P-c (with the van der Waals surface area) and the cubic EoS at a single experimental vapor-pressure point (e.g., the normal boiling point). We have employed a modified version of the Peng-Robinson EoS, but we have verified that any cubic EoS yields similar results at least for n-alkanes up to n-octacosane (MW = 394). The method is applied to the prediction of vapor pressures for several nonpolar and slightly polar heavy compounds with very satisfactory results, essentially independent of the experimental point used. Furthermore, the method yields critical properties for heavy alkanes (N-c > 20) and other compounds which are in very good agreement with recent available experimental data.