A method is given that uses Hugoniot data iin the mixed-phase regime to constrain further equation of state (EOS) parameters of low- and high-pressure phases of materials undergoing phase transformations on shock loading. We compute the relative proportion of low- and high-pressure phases present in the mixed-phase region and apply additional tests to the EOS parameters of the separate low- and high-pressure phases by invoking two simple requirements: the fraction of high-pressure phase (1) must increase with increasing shock pressure, and (2) must approacch one at the high-pressure end of the mixed-phase regime. We apply our analysis to previously published data for potassium thioferrite, KFeS2, and pyrhotite, Fe0.9S. We find that including the mixed-phase regime data in the KFeS2 analysis requires no change in the published high-pressure EOS parameters. For Fe0.9S we must modify the high-pressure phase EOS parameters to account for both the mixed-phase and high-pressure phase Hugoniot data. Our values of zero-pressure density, bulk modulus and first pressure derivative of the bulk modulus of the high-pressure phase of Fe0.9S are 5.3 Mg/m3, 106 GPa, and 4.9, respectively.