A method of operating a multi-cylinder compression ignition engine having at least one cylinder acting as a compression cylinder and at least one cylinder action as a combustion cylinder. The method comprise compressing air in the compression cylinder, and in the combustion cylinder, opening and then closing an exhaust valve during an exhaust stroke to trap some exhaust gas, during a compression stoke immediately following the exhaust stroke, injecting a controlled amount of fuel into the combustion chamber to obtain compression ignition at or near a top dead center piston position without reaching combustion temperatures at which NOX is formed, and injecting compressed air and fuel during a power stroke immediately following the compression stroke to sustain combustion to burn the fuel with an equivalence ratio within a predetermined range around unity. Various embodiments are disclosed.