Systematic impurity doping in the Cu-0 plane of the hole-doped cuprate
superconductors may allow one to decide between unconventional (''d-w
ave'') and anisotropic conventional (''s-wave'') states as possible ca
ndidates for the order parameter in these materials. We show that pote
ntial scattering of any strength always increases the gap minima of su
ch s-wave states, leading to activated behavior in temperature with ch
aracteristic impurity concentration dependence in observable quantitie
s such as the penetration depth. A magnetic component to the scatterin
g may destroy the energy gap and give rise to conventional gapless beh
avior, or lead to a nonmonotonic dependence of the gap on impurity con
centration. We discuss how experiments constrain this analysis.