  Systematic impurity doping in the Cu-O plane of the hole-doped cuprate
superconductors may allow one to decide between unconvention al ("d-wave") and
anisotropic conventional ("s-wave") states as possible candidates for the order
parameter in these materials. We show that potential scattering of any strength
always increases the gap minima of such s-wave states, leading to activated
behavior in temperature with characteristic impurity concentration dependence
in observable quantities such as the penetration depth. A magnetic component to
the scattering may destroy the energy gap and give rise to conventional gapless
behavior, or lead to a nonmonotonic dependence of the gap on impurity
concentration. We discuss how experiments constrain this analysis.
