The use of absolute-admittance measurements has been limited in the past to the determination of parameters of relatively high-Q resonators. By allowing only one major assumption in the analysis of the resonator, new equations are developed which consider the mechanical loss to be a first-order effect. On the basis of extensive numerical calculations of resonator characteristics in which no approximations were made, the errors of both the conventional relationships and the new equations are made evident. It is found that these new equations materially extend the usefulness of this method of measurement to include systems for which the mechanical Q is lower than the capacitance ratio. For the extreme case exemplified by a barium titanate ceramic resonator in air, the conventional calculation method introduces errors of approximately fifty percent in some of the crystal parameters as compared to errors of one percent for the new equations. The improvement is less significant in the determination of the parameters of underwater sound transducers.