  A framework is presented for including second-order perturbative corrections
to the radiation patterns of parton showers. The formalism allows to combine
O(alphaS^2)-corrected iterated 2->3 kernels for "ordered" gluon emissions with
tree-level 2->4 kernels for "unordered" ones. The combined Sudakov evolution
kernel is thus accurate to O(alphaS^2). As a first step towards a full-fledged
implementation of these ideas, we develop an explicit implementation of 2->4
shower branchings in this letter.
