An internal combustion engine can be operated in an efficiency mode to provide a first power output range between zero and a transition power output level and in a power mode to provide a second power output range between the transition power output level and a maximum power output level. A first ignition timing and a first air/fuel ratio of the mixture can be used in the efficiency mode to avoid premature auto-ignition of a mixture of inlet air and a fuel according to an octane rating of the fuel and a compression ratio exceeding approximately 13:1. A second ignition timing and a second air/fuel ratio of the mixture can be used in the power mode to avoid premature auto-ignition of the mixture according to the octane rating of the fuel and the compression ratio exceeding approximately 13: 1. To further enable knock free operation of such an engine, turbulence can be imparted to the mixture to promote a faster burn duration and high temperatures that may lead to premature auto-ignition of the mixture can be avoided.