  We discuss the weak-coupling BCS theory of a superconductor with the
impurities, accounting for their anisotropic momentum-dependent potential. The
impurity scattering process is considered in the t-matrix approximation and its
influence on the superconducting critical temperature is studied in the Born
and unitary limit for a d- and (d+s)-wave superconductors. We observe a
significant dependence of the pair-breaking strength on the symmetry of the
scattering potential and classify the impurity potentials according to their
ability to alter T_c. A good agreement with the experimental data for Zn doping
and oxygen irradiation in the overdoped cuprates is found.
