The authors show that by folding data from an n*n mesh onto an n*(n/k) submesh, sorting on the submesh, and finally unfolding back onto the entire n*n mesh it is possible to sort on bidirectional and strict unidirectional meshes using a number of routing steps that is very close to the distance lower bound for these architectures. The technique may also be applied to reconfigurable bus architectures to obtain faster sorting algorithms.