Atmospheric neutrino anomaly without maximal mixing?

We consider a pattern of neutrino masses in which there is an approximate mass degeneracy between the two mass eigenstates most coupled to the nu /sub mu / and nu /sub tau / flavor eigenstates. Earth-matter effects can lift this degeneracy and induce an effectively maximal mixing between these two generations. This occurs if nu /sub e/'s contain comparable admixtures of the degenerate eigenstates, even if they are not large. This provides an explanation of the atmospheric neutrino anomaly in which the ab initio introduction of a large mixing angle is not required. To test this possibility we perform a detailed analysis of the 52 kiloton-year SuperKamiokande data, and we find that in a large region of parameter space the corresponding confidence levels are excellent. 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 the data.