The specific-heat jump Δ C at a critical temperature T_c in an anisotropic superconductor containing both potential and spin-flip scatterers is calculated within a weak-coupling mean-field approximation. It is shown that the presence of even a small amount of spin-flip scatterers in the sample leads to a drastic change in the dependence of Δ C on T_c in a disordered (d+s)-wave or a strongly anisotropic s-wave superconductor. The implications for experimental tests for the presence of an s-wave

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... dmixture in the superconducting order parameter of high-T_c superconductors are discussed.