A linear least-squares fit of a finite-strain equation of state to pressure-density measurement is possible even when the initial density is unknown. This provides an objective extrapolation of data on a high-pressure phase to zero pressure, and the zero-pressure density and elastic properties (as well as their uncertainties) can be directly estimated . For typical uncertainties in ultrahigh pressure diamond-cell experiments compression data extending over strains of the high-pressure phase of at least 0.04 and 0.11 (i.e., compression ranges, Δ&rgr;/&rgr;, of at least 12% and 35%) are required in order to constrain, respectively, third-and fourth-order contributions to the equation of state.