  We calculate the first-order perturbative correction to the transition
temperature $T_c$ in a superconductor with both non-magnetic and magnetic
impurities. We do this by first evaluating the correction to the effective
potential, $\Omega(\Delta)$, and then obtain the first-order correction to the
order parameter, $\Delta$, by finding the minimum of $\Omega(\Delta)$. Setting
$\Delta=0$ finally allows $T_c$ to be evaluated. $T_c$ is now a function of
both the resistance per square, $R_\square$, a measure of the non-magnetic
disorder, and the spin-flip scattering rate, $1/\tau_s$, a measure of the
magnetic disorder. We find that the effective pair-breaking rate per magnetic
impurity is virtually independent of the resistance per square of the film, in
agreement with an experiment of Chervenak and Valles. This conclusion is
supported by both the perturbative calculation, and by a non-perturbative
re-summation technique.
