Segment-segment interaction models, such as the simplified-perturbed-hard-chain theory (SPHCT) equation of state (EOS), offer the potential of improved volumetric and equilibrium property predictions. Our previous evaluations of the SPHCT EOS and similar evaluations in the literature lead us to believe that proper modifications can make the SPHCT more accurate. In the present study, we report our results for pure-fluid property predictions. The SPHCT EOS is reduced from a three-parameter to a one-parameter equation of state by using classical critical point constraints. The temperature dependence of the attractive portion of the equation is modified to provide improved vapor pressure predictions. In addition, volumetric predictions are enhanced by incorporating a phenomenological volume translation strategy. The modified SPHCT equation of state is compared with the original version and with the Peng-Robinson (PR) equation using experimental data for a variety of chemical species. The modified SPHCT equation yields better vapor pressure predictions than either the original SPHCT or PR equations (1.2% average absolute percent deviation for the modified SPHCT, 3.4% for the original SPHCT, and 4.2% for PR). Improved results are also obtained for liquid and vapor phase densities (2.7% and 1.9% for the modified SPHCT, 6.8% and 6.2% far the original SPHCT, and 6.6% and 3.1% for PR for liquid and vapor phases respectively).