There is provided an ex vivo method for reducing the immunogenicity of a tissue or organ prior to transplantation, comprising:(a) establishing the tissue or organ in a warm perfusion system capable of supporting oxidative metabolism of the tissue or organ(b) perfusing the tissue or organ with a warm non-blood perfusion solution for at least 1 hour to allow passenger leukocytes within the tissue or organ to migrate from the tissue or organ into the recirculating perfusion solution(c) isolating the passenger leukocytes from the recirculating perfusion solution to prevent the passenger leukocytes from re-entering the tissue or organ.