Combustion engines are typically only 20-30% efficient at part-load operating conditions, resulting in poor fuel economy on average. To address this, LiquidPiston has developed an improved thermodynamics cycle, called the High-Efficiency Hybrid Cycle (HEHC), which optimizes each process (stroke) of the engine operation, with the aim of maximizing fuel efficiency. The cycle consists of: 1) a high compression ratio; 2) constant-volume combustion, and 3) over-expansion. At a modest compression ratio of 18:1, this cycle offers an ideal thermodynamic efficiency of 74%. To embody the HEHC cycle, LiquidPiston has developed two very different rotary engine architectures ? called the ?M? and ?X? engines. These rotary engine architectures offer flexibility in executing the thermodynamics cycle, and also result in a very compact package. In this talk, I will present recent results in the development of the LiquidPiston engines. The company is currently testing 20 and 40 HP versions of the ?M?