  The specific-heat jump $\Delta C$ 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 $\Delta C$ 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 admixture in the
superconducting order parameter of high-$T_c$ superconductors are discussed.
