  Greg McShane introduced a remarkable identity for lengths of simple closed
geodesics on the once punctured torus with a complete, finite volume hyperbolic
structure. Bowditch later generalized this and gave sufficient conditions for
the identity to hold for general type-preserving representations of a free
group on two generators \Gamma to SL(2,C). In this note we extend Bowditch's
result by giving necessary and sufficient conditions for the identity to hold,
and also for the generalized McShane identity to hold for arbitrary (not
necessarily type preserving) representations. We also give a version of
Bowditch's variation of McShane's identity to once-punctured torus bundles, to
the case where the monodromy is generated by a reducible element, and provide
necessary and sufficient conditions for the variation to hold.
