The High Efficiency Hybrid Cycle (HEHC) is a thermodynamic cycle which borrows elements of Diesel, Otto and Atkinson cycles, including: Air compression to a high ratio, followed by fuel injection and compression ignition (Diesel). Constant volume combustion (Otto) Over-expansion (Atkinson) Optionally, internal cooling heat recovery via steam generation (Rankine). Simple air standard analysis predicts this cycle to be 17% more efficient than diesel and 19% more efficient than Otto. The construction of a prototype rotary engine implementing this cycle is also described in detail. The main engine components consist of a rotor in pure rotation and two reciprocating gates directly driven by overhead cams. This combination separates the working mixture into three separate volumes. At a given rotor position each volume operates at a different part of the cycle. For instance, intake/compression, combustion, expansion/exhaust are occurring simultaneously in separate chambers. As the rotor moves, the cavity formed by the side of the rotor, the retracting compressor gate, and the stationary housing is decreasing in volume, producing compression. The gate fully retracts, as the rotor passes beneath. The air is fully compressed into a combustion chamber within the housing and held at constant volume. Fuel is injected, and combustion occurs at relatively constant volume. As the rotor continues its motion, the volume defined by the housing, expander-gate, and the rotor is increasing through the completion of the expansion stroke. Due to the geometry, a higher expansion ratio is achieved relative to the compression ratio. The result is a high power density, high speed engine. A 20 HP prototype is currently being tested. Predicted output is 143 Hp/L and 30% thermal efficiency.