Matching donations from deceased patients to patients on the waiting list account for over 85\% of all kidney transplants performed in Australia. We propose a simple mechanisms to perform this matching and compare this new mechanism with the more complex algorithm currently under consideration by the Organ and Tissue Authority in Australia. We perform a number of experiments using real world data provided by the Organ and Tissue Authority of Australia. We find that our simple mechanism is more efficient and fairer in practice compared to the other mechanism currently under consideration.