Insights from the venerable Trouton's Rule have been used to guide the development of an applied-thermodynamic method for the estimation, correlation, and evaluation of pure-component vapor pressure. Trouton's Rule very simply and succinctly states that the entropy of vaporization of fluids at their normal boiling point is a constant (approximate to 10.5 times the gas constant). Detailed evaluation of the data for many families of chemical compounds reveals the subtle patterns of departures from the rule, and facilitates the development of a useful new correlation. Several examples are presented to demonstrate the value of the new correlation to estimate, correlate, extrapolate, and evaluate vapor-pressure data, and to understand the patterns of vapor-pressure behavior. The methodology provides a guide for the development of thermodynamic correlations, and the resulting correlations are expected to be useful for the practice of applied thermodynamics.