Vapor pressure, heat of vaporization, liquid heat capacity, and ideal-gas heat capacity for pure compounds between the triple point and critical point are important properties for process design and optimization. These thermophysical properties are related to each other through temperature derivatives of thermodynamic relationships stemming from a temperature-dependent vapor-pressure correlation. The Riedel equation has been considered to be an excellent and simple choice among vapor-pressure correlating equations [Velasco et al. J. Chem. Thermodyn. 2008, 40 (5), 789−797] but requires modification of the final coefficient to provide thermodynamic consistency with thermal data [Hogge et al. Fluid Phase Equilib. 2016, 429, 149−165]. New predictive correlations with final coefficients in integer steps from 1 to 6 have been created for compounds with limited or no vaporpressure data, based on the methodology used originally by Riedel [Chem. Ing. Tech. 1954, 26 (2), 83−89]. Liquid heat capacity was predicted using these vapor-pressure correlations, and the best final coefficient values were chosen based on the ability to simultaneously represent vapor pressure and liquid heat capacity. This procedure improves the fit to liquid heat-capacity data by 5−10% (average absolute deviation), while maintaining the fit of vapor-pressure data similar to those of other prediction methods. Additionally, low-temperature vapor-pressure predictions were improved by relying on liquid heat-capacity data.