A concept adding two strokes to the Otto or Diesel engine cycle to increase fuel efficiency is presented here. It can be thought of as a four-stroke Otto or Diesel cycle followed by a two-stroke heat recovery steam cycle. A partial exhaust event coupled with water injection adds an additional power stroke. Waste heat from two sources is effectively converted into usable work: engine coolant and exhaust gas. An ideal thermodynamics model of the exhaust gas compression, water injection and expansion was used to investigate this modification. By changing the exhaust valve closing timing during the exhaust stroke, the optimum amount of exhaust can be recompressed, maximizing the net mean effective pressure of the steam expansion stroke (MEPsteam). The valve closing timing for maximum MEPsteam is limited by either 1 bar or the dew point temperature of the expansion gas/moisture mixture when the exhaust valve opens. The range of MEPsteam calculated for the geometry of a conventional gasoline engine and is from 0.75 to 2.5 bars. Typical combustion mean effective pressures (MEPcombustion) Of naturally aspirated gasoline engines are up to 10 bar, thus this concept has the potential to significantly increase the engine efficiency and fuel economy. (C) 2009 Elsevier Ltd. All rights reserved.