Improvement in the prediction of very low vapor pressures is checked by introducing heat capacity data into the estimation of cubic equation-of-state (EOS) parameters. As the key parameter is the temperature-dependent parameter a, several expressions (mainly of exponential form) were investigated. All of them were chosen in order to show a consistent behavior for the two considered properties (vapor pressures and heat capacities). The cubic EOS used as an illustration is of the Peng-Robinson type applied to heavy hydrocarbons. No satisfactory refinement in the prediction of the very low vapor pressures was observed in comparison with the results obtained by extrapolating the EOS from medium to very low pressures. This work has, however, the following benefits: (1) to point out the changes that should be made to improve these predictions; (2) to inform on the accuracy that may be obtained if vapor pressures of heavy organic compounds are predicted from heat capacity data as the sole alternative for estimating the temperature-dependent parameter a of a cubic EOS; (3) to confirm the reliability of the cubic group-contribution (GC)-based EOS proposed by Coniglio et al. [Ind. Eng. Chem. Res. 39 (2000) 5037] when extrapolated for modeling crude oils or gas condensates encountered in the petroleum industry.