We consider a pattern of neutrino masses in which there is an approximate m
ass degeneracy between the two mass eigenstates most coupled to the v(mu) a
nd v(tau) flavor eigenstates. Earth-matter effects can lift this degeneracy
and induce an effectively maximal mixing between these two generations. Th
is occurs if v(e)'s contain comparable admixtures of the degenerate eigenst
ates, even if they are not large. This provides an explanation of the atmos
pheric neutrino anomaly in which the ab initio introduction of a large mixi
ng angle is not required. To test this possibility we perform a detailed an
alysis of the 52 kiloton-year SuperKamiokande data, and we find that in a l
arge region of parameter space the corresponding confidence levels are exce
llent. The most recent results from the CHOOZ reactor experiment, however,
severely curtail this region, so that the conventional scenario with nearly
maximal mixing angles, which we also analyze in detail, is supported by th
e data.