We present a reanalysis of direct CP violation in the decay K-L-->pi (+)pi
(-)gamma. We point out an existing discrepancy between the theoretical and
experimental definitions of epsilon (+-gamma)'. Adopting the experimental d
efinition of epsilon (+-gamma)' we estimate that epsilon (+-gamma)'/epsilon
could be as large as a few times 10(-4) both within the standard model and
beyond. We discuss these estimates in detail and we also show how a judici
ous choice of E-gamma* cuts can increase the sensitivity of the observable
epsilon (+-gamma)' to the underlying CP violation.