  Recently we proposed a framework for explaining the observed evidence for
neutrino oscillations without enlarging the neutrino sector, by introducing CPT
violating Dirac masses for the neutrinos. In this paper we continue the
exploration of the phenomenology of CPT violation in the neutrino sector. We
show that our CPT violating model fits the existing SuperKamiokande data at
least as well as the standard atmospheric neutrino oscillation models. We
discuss the challenge of measuring CP violation in a neutrino sector that also
violates CPT. We point out that the proposed off-axis extension of MINOS looks
especially promising in this regard. Finally, we describe a method to compute
CPT violating neutrino effects by mocking them up with analog matter effects.
