Mixed cycle compression ignition engines and methods of operating a camless compression ignition engine by establishing a number of operating cycles for operating the engine, each for a particular engine load range and storing a respective algorithm and engine operating parameters for each operating cycle in a lookup table, receiving engine operating information, including piston position when compression ignition occurs, receiving a power setting for the engine, selecting from the lookup table, an algorithm and operating parameters for an operating cycle for the engine applicable to that power setting, operating the engine using the selected algorithm and operating parameters, and adjusting the engine operating parameters based on received engine operating information. Various operating cycles are disclosed.