A method of operating an engine system should produce relatively low concentrations of various emissions without compromising a desired power output of the system. In order to operate an engine system of the present disclosure, a predetermined total amount of fuel injected into at least one combustion chamber is apportioned into at least a first amount and a second amount of fuel. The first amount of fuel is injected into the at least one combustion chamber during non-auto ignition conditions. The second amount of fuel is injected into the at least one combustion chamber during auto-ignition conditions. When the engine system is in a mid-low engine load range, the second amount of fuel is one of equal to or less than 15% of the predetermined total amount of fuel. When the engine system is in a high engine load range, the second amount of fuel is greater than 15% of the predetermined total amount of fuel.