A compression ignition engine uses two or more fuel charges having two or more reactivities to control the timing and duration of combustion. In a preferred implementation, a lower-reactivity fuel charge is injected or otherwise introduced into the combustion chamber, preferably sufficiently early that it becomes at least substantially homogeneously dispersed within the chamber before a subsequent injection is made. One or more subsequent injections of higher-reactivity fuel charges are then made, and these preferably distribute the higher-reactivity matter within the lower-reactivity chamber space such that combustion begins in the higher-reactivity regions, and with the lower-reactivity regions following thereafter. By appropriately choosing the reactivities of the charges, their relative amounts, and their timing, combustion can be tailored to achieve optimal power output (and thus fuel efficiency), at controlled temperatures (and thus controlled NOx), and with controlled equivalence ratios (and thus controlled soot).