  Agreement between the experimental value $\Gamma (K_S\rightarrow
\gamma\gamma)$ and the number predicted via a one-loop chiral perturbation
theory calculation has been cited as a success for the latter. On the other
hand the one-loop prediction for the closely related process $K_L\rightarrow
\pi^0\gamma\gamma$ has been found to be a factor three below the experimental
value. Using the inputs of unitarity and dispersion relations, we demonstrate
the importance of higher order loop effects to both of these processes.
