This article explores the relations between the cycle performance and the main operating parameters of the Allam cycle with uncooled turbine through a simplified thermodynamic analysis. The cycle efficiency is maximized with respect to turbine parameters. Expressions are derived for the estimation of optimum turbine inlet temperature (TIT) and pressure as well as optimum turbine exhaust pressure. The cryogenic air separation process developed by Allam is employed, which produces supercritical oxygen at combustion pressure. Typical numerical results are presented using the new expressions for optimum turbine parameters. The highest cycle efficiency is found to be 66.4% at a TIT/inlet pressure/exhaust pressure of 1306 K/300 bar/39.4 bar and a CO2 compressor exit pressure of 60 bar. The newly derived relationships for the key process parameters allow a better understanding of the operation of the Allam cycle.