A power supply and method for operating a power supply for a short arc lamp are provided herein. The power supply and method can operate to provide to a number of advantageous operations. One aspect herein provides a power supply which utilizes a constant power mode type of operation. However, the constant power mode is modified to allow for some variation in power in order to provide for a more constant light output by the lamp. A second aspect herein provides for controlling the operation of a boost voltage applied to the lamp at start up. This control allows for adjusting the applied boost voltage to accommodate the changing characteristics of the lamp itself, and these adjustments can allow for extended life of the lamp.