Abstract: A mathematical model to optimize protocols for the addition or removal of cryoprotectant to or from sperm cells. This disclosure describes the use of four equations to predict optimal protocols to add or remove cryoprotectant to or from sperm cells. The equations particularly require experimentally found data, specific to a species of sperm, regarding the osmotic tolerance of sperm cells, where osmotic tolerance refers to the sperm cells ability to shrink or swell to various changes in osmolality without injury. The equations further require the cryoprotectant permeability coefficient and the water permeability coefficient of the particular sperm cells' plasma membrane. Also disclosed are two particularly preferred methods to add or remove cryoprotectant to or from sperm. These preferred methods are Fixed-Volume-Step addition/removal of cryoprotectant or Fixed-Molarity-Step addition/removal of cryoprotectant.