We design a flexible algorithm that exploits deceased donor kidneys to initiate chains of living donor kidney paired donations, combining deceased and living donor allocation mechanisms to improve the quantity and quality of kidney transplants. The advantages of this approach have been measured using retrospective data on the pool of donor/recipient incompatible and desensitized pairs at the Padua University Hospital, the largest center for living donor kidney transplants in Italy. The experiments show a remarkable improvement on the number of patients with incompatible donor who could be transplanted, a decrease in the number of desensitization procedures, and an increase in the number of UT patients (that is, patients unlikely to be transplanted for immunological reasons) in the waiting list who could receive an organ.