We contrast the effects of non-magnetic impurities on the properties of
superconductors having a \dw\ order parameter, and a highly anisotropic s-wave
(ASW) gap with the same nodal structure. The non-vanishing, impurity induced,
off-diagonal self-energy in the ASW state is shown to gap out the low energy
excitations present in the clean system, leading to a qualitatively different
impurity response of the single particle density of states compared to the \dw\
state. We discuss how this behaviour can be employed to distinguish one state
from the other by an analysis of high-resolution angle-resolved photoemission
spectra.Comment: 12 pages, uuencoded Postscrip