This paper reports the thermodynamic optimization based on the maximum mean effective pressure, maximum power and maximum thermal efficiency criteria for an irreversible Otto heat engine model which includes internal irreversibility resulting from the adiabatic processes. The mean effective pressure, power output, and thermal efficiency are obtained by introducing the compression ratio, cycle temperature ratio, specific heat ratio and the compression and expansion efficiencies. Optimal performance and design parameters of the Otto cycle are obtained analytically for the maximum power and maximum thermal efficiency conditions and numerically for the maximum mean effective pressure conditions. The results at maximum mean effective pressure conditions are compared with those results obtained by using the maximum power and maximum thermal efficiency criteria. The effects of the cycle temperature ratio and cycle pressure ratio on the general and optimal performances are investigated.