System, methods, and computer-readable media. A method performed by a mail sorting machine includes receiving a plurality of mailpieces in an input of the mail sorting machine and sorting the mailpieces into a plurality of sequencing groups. The method includes storing a first subset of the mailpieces in each sequencing group. The method includes sorting a second subset of the mailpieces in each sequencing group to a plurality of outlets, where storing the first subset and sorting the second subset are performed for each sequencing group by processing each sequentially in a group order. The method includes sorting the stored first subset mailpieces to the plurality of outlets.