Organs transplanted between phylogenetically disparate species, such as from the pig into the primate, are subject to intragraft deposition of preformed recipient immunoglobulin M (IgM) antibodies with subsequent complement activation finally leading to complete and rapid destruction of the xenograft (hyperacute graft rejection, HAR). Current therapeutic strategies for abrogation of HAR include pretransplant antibody absorption by specific or nonspecific extracorporeal column perfusion, ex vivo donor organ perfusion, the administration of substances interfering with complement activation, or even the genetic alteration of the donor. Here, in the pig to cynomolgus monkey species combination, we are describing an experimental model for abrogation of HAR by using large, relative to the recipient weight, oversized donor kidneys as xenotransplants. Porcine kidney xenotransplantation (n = 15) was performed using large white pigs of different weights and ages as organ donors and cynomolgus monkeys as recipients. In grafts with an organ weight below 50 g (20 to 48 g, median 25 g), primary nonfunction (PNF) of the porcine kidney was observed in 11 out of 12 cases and complete HAR in 5 out of 12 experiments. In contrast, none of three grafts with a donor organ weight >70 g showed signs of HAR or PNF. In one animal, a second porcine kidney from the same donor (23 g) was successfully transplanted immediately after HAR and subsequent removal of a first porcine kidney (20 g). By using appropriate immunohistochemistry stainings of reperfusion biopsies, profound deposition of recipient natural antibodies in both small and large xenografts was shown, with only scarce deposition of C3 and C5b-9 in the latter, indicating only incomplete intragraft activation of the complement cascade in these organs. Intraoperative cardiac output (CO) measurements performed in 7 experiments demonstrated a 20 to 50% decrease in CO following reperfusion in 6 out of 7 grafts irrespective of the donor organ weight. The intraoperative decrease in CO was not associated with perioperative morbidity or mortality. The use of oversized doner kidneys can enable the study of a variety of immunologic and physiologic sequela beyond HAR associated with life-supporting discordant primate kidney transplantation.