Improved transient response times are obtained while maintaining low emissions with a low pressure EGR system through methods for quickly obtaining a desired oxygen concentration for charge-air to be used for combustion. Under a first method, fuel quantity in the main combustion event is controlled in the combustion process to produce exhaust around a relatively constant target exhaust oxygen concentration value. By keeping the exhaust oxygen concentration levels at a relatively constant value, lag time in waiting for low pressure EGR valve adjustments during transients may be avoided, and the system's air handling response to meet transients may be paced solely by adjusting the mass of air to be supplied (i.e. boost response). Under a second method, a multiple-stage combustion process is utilized, in which fuel feed is controlled in a small, preliminary HCCI-type combustion event in order to produce a target oxygen concentration of charge-air to be used for the second, main combustion event. Under a third method, exhaust rebreathing is used to produce a target oxygen concentration of charge-air to be used for combustion.