  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
definition 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 judicious
choice of E_gamma cuts can increase the sensitivity of the observable
epsilon'_{+-\gamma} to the underlying CP violation.
