A theoretical investigation to optimize thermoelectric elements for thermoelectric coolers was performed using a new one-dimensional analytic model. Mathematical expressions for the optimum current and the optimum length of a thermoelectric element, which maximize the coefficient of performance of thermoelectric coolers, were obtained. The optimum current is expressed in terms of the cooling load for a thermoelectric element, the hot and cold side temperatures and thermoelectric properties, but not the length of a thermoelectric element. The optimum current is proportional to the cooling load and decreases as the temperature difference between the hot and cold sides decreases. It is also shown that the optimum length of a thermoelectric element decreases as the cooling load increases.