In the calculation of K ° ~ yy to first order in SU(3) breaking, one must include not only ~/-rg mixing but also the first-order corrections to the SU(3) relations for the K --, ~/ and 71 --, y/ transitions. We calculate the leading corrections to these processes at one loop in chiral perturbation theory. Although not large in themselves, they can have potentially large effects in K --* yy due to the cancellations among the leading SU(3) invariant terms. We also comment on corresponding effects on the dispersive part of the K c - K s mass differences.