The exhaust gas from an internal combustion engine contains approximately 30% of the thermal energy of combustion. Waste heat-recovery systems aim to reclaim a proportion of this energy in a bottoming thermodynamic cycle to raise the overall system thermal efficiency. The inverted Brayton cycle (IBC) considered as a potential exhaust-gas heat-recovery system is a little-studied approach, especially when applied to small automotive power plants. Hence, a model of an air-standard, irreversible Otto cycle and the IBC using finite-time thermodynamics (FTT) is presented to study heat recovery applied to an automotive internal combustion engine. The other two alternatives power cycles, the pressurized Brayton cycle and the turbocompounding system (TS), are compared with the IBC to specify the strengths and weaknesses of three alternative cycles. In the current paper, an irreversible Otto-cycle model with an array of losses is used as a base for the bottoming cycle. The deviation of the turbomachinery from the idealized behavior is described by the isentropic component efficiencies. The performance of the system as defined as the specific power output and thermal efficiency is considered using parametric studies. The results show that the performance of the IBC can be positively affected by five critical parameters—the number of compression stages, the cycle inlet temperature and pressure, the isentropic efficiency of the turbomachinery, and the effectiveness of the heat exchanger. There exists an optimum pressure ratio across the IBC turbine that delivers the maximum specific power. In view of the specific power, installing a single-stage of the IBC appears to be the best balance between performance and complexity. Three alternative cycles are compared in terms of the thermal efficiency. The results indicate that the pressurized and IBCs can improve the performance of the turbocharged engine (TCE) only when the turbomachinery efficiencies are higher than a value which changes with the operating condition. High performance of the IBC turbomachinery is required to ensure that the TCE with the IBC is superior to that with TS.