This work is based on calculations about extreme mean effective and maximum pressures which were published earlier by the author and colleagues. The motivation for the work presented in this paper is to reduce the maximum pressure while keeping a high mep without sacrificing efficiency. It is investigated in a theoretical study in how far this can be accomplished via turbocompounding.The basis is a 320 mm bore four stroke medium speed engine. It is equipped with a state-of-the-art two stage turbocharging system.As a first step turbocompounding is investigated for mean effective pressures from 22 to 80 bar. The bsfc of the turbocharged engine is in the range of 175 to 185 g/kWh depending on mep. With turbocompounding the exhaust pressure before turbine is optimised and figures between 160 and 165 g/kWh are reached. Thermal loading of the engine increases.In the second step strategies to reduce maximum pressure are investigated for an mep of ca. 50 bar. Reduced compression ratio and retarded injection increase the optimum bsfc of the turbocompound engine slightly while a reduced air-fuel-ratio reduces it. With a combination of all three measures maximum pressure can be reduced from 425 to 225 bar while keeping bsfc below 165 g/kWh.The small dependence of bsfc on maximum pressure results because the turbines of the turbocompound engine can utilize the exhaust energy better than those of the turbocharged one. An alternative explanation is found if the Joule cycle is used as the reference cycle for the turbocompound engine.