The "universal" equation of state recently proposed by Vinet, Ferrante, Rose, and Smith is numerically equivalent, to leading order in finite strain, to several well-established two-parameter equations of state. Notably, it is in accord with the Birch-Murnaghan equation that is derived from Eulerian finite-strain theory, and hence is applicable to condensed matter involving any bonding type. It is well established that the Eulerian finite-strain formalism is exceptionally successful in describing the compressional behavior of materials at high pressures. This argues strongly in favor of the conclusion of Vinet and co-workers that their equation of state is universal in the sense of successfully reproducing the pressure-volume relations of a wide variety of materials. It appears, however, that no existing two-parameter equation of state is fully in accord with all measurements of high-order elastic moduli. In detail, published values of compressional moduli imply that deviations from the "universal" and Birch-Murnaghan equations of state exist, but these can be accounted for with higher-order terms.