We consider a Paired Kidney Exchange (PKE) model in which patients’ preferences are restricted so that patients prefer kidneys from compatible younger donors to kidneys from older ones. We propose a family of rules, sequential priority rules, that only allow for pairwise exchanges and satisfy individual rationality, efficiency, strategy-proofness, and non-bossiness. These rules allocate kidneys according to a priority algorithm that gives priority to patients with younger donors and assign kidneys from younger donors first. We extend the analysis to rules that allow multiple ways exchanges and to the case of patients who have more than one potential donor.