Introduces a model of a mesh-connected computer in which multiple-key packets can be exchanged between processors in single routing steps. The author develops a sorting algorithm for such an enhanced model, which has time performance better than optimal algorithms in the traditional model. The technical contributions of this paper are as follows. The first is a new 5n-o(n) lower bound for sorting in a row-major ordering. This improves the best previously known bound of 4n-4. The second contribution is a new sorting algorithm utilizing multiple-packet routing capabilities. The time complexity of this algorithm, measured in the number of concurrent routing steps, can be arbitrarily close to the absolute distance lower bound of 2n-2, provided the number of keys that fit in one routing packet is sufficiently large.