This paper reviews some possible design criteria for the permutation P in a DES style cryptosystem. These permutations provide the diffusion component in a substitution-permutation network. Some empirical rules which seem to account for the derivation of the permutation used in the DES are first presented. Then it is noted that these permutations may be regarded as latin-squares which link the outputs of S-boxes to their inputs at the next stage. A subset of these with a regular structure, and which perform well in a dependency analysis are then presented. Some design rules are then derived, and it is suggested these be used to design permutations in future schemes for an extended version of the DES.