At pressures below similar to 55 MPa, the perturbed chain - statistically associated fluid theory (PC-SAFT) gives reliable density predictions within +/- 2% for n-alkanes and other hydrocarbons. However, PC-SAFT tends to over-predict density values by as much as 5% at higher pressures, particularly for normal and branched alkalies. For many compounds, literature values for the three pure-component PC-SAFT parameters m, sigma, and epsilon/k(B) are typically obtained by fitting the equation to sub-critical P rho T data or occasionally both sub-critical and supercritical density data. A new set of pure-component PC-SAFT parameters for density prediction at extreme conditions is reported here by fitting the PC-SAFT equation to single-component density data collected at temperatures from ambient to 533 K and pressures from similar to 6.9 to 276 MPa, rather than sub-critical density data since these high temperature, high pressure (HTHP) conditions are similar to conditions typically associated with petroleum recovery from ultra-deep formations. Density predictions made using the new, HTHP PC-SAFT pure-component parameters at HTHP conditions are clearly superior to those obtained using the original PC-SAFT parameters. Although a correction term can be applied to the epsilon/k(B) parameter to make HTHP PC-SAFT pure-component density predictions at pressures below 6.9 MPa only slightly inferior to predictions with the original PC-SAFT parameters, vapor-liquid equilibrium predictions with the original PC-SAFT parameters are clearly superior to predictions made with the HTHP parameters. Correlations are developed to accurately predict the HTHP PC-SAFT parameters for normal and branched alkanes for which there are either incomplete or nonexistent experimental density data sets. (C) 2012 Elsevier B.V. All rights reserved.