In this article, power and efficiency analysis of irreversible Brayton cycle, which is one of the well-known heat engine cycles by the undergraduates, are carried out based on alternative criteria. Power, power density, and efficient power optimizations are also realized and the thermal efficiencies of the cycle are determined at maximum power and efficiency outputs. The efficient power is relatively new criterion and defined as the multiplication of power by efficiency. Therefore, this criterion considers not only the power output but also the cycle efficiency. Maximizing the efficient power function gives a compromise between power and efficiency. The effects of the external irreversibilities on the performances are investigated for various cycle parameters.