A compression ignition engine (10) operates to fuel an engine cylinder (12) to create an in-cylinder air-fuel charge and to cause that charge to autoignite. A fuel injector (20) operates to inject fuel into the engine cylinder for substantially the entire duration of a first phase (24) of fuel injection at substantially the maximum injection pressure that the fuel injector can deliver to create a premixed fraction of the in-cylinder air-fuel charge prior to autoignition. As the first phase ends, fuel injection transitions to a second phase (26) which commences in advance of autoignition. During the second phase, the fuel injector injects fuel into the engine cylinder at a rate of injection that is significantly less than the rate of injection used during the first phase.