The invention provides a method for operating a multi-cylinder, spark-ignition, and direct-injection, four-stroke internal - combustion engine adapted to operate in a controlled auto-ignition mode selectively operative at stoichiometry and lean of stoichiometry. The method comprises adapting an engine valve actuation system to control engine valve opening and closing, and monitoring engine operating conditions and ambient barometric pressure. The engine is operated unthrottled and the engine valve actuation system is controlled to effect a negative valve overlap period when the engine operating conditions are within predetermined ranges. A mass of fuel is injected during the negative valve overlap period. The magnitude of the negative valve overlap period is decreased with decreasing ambient pressure and increased with increasing ambient pressure.