A direct injection controlled auto-ignition engine is operated at steady state, within a homogeneous charge compression-ignition (HCCI) load range and with fuel-air-diluent mixtures at predetermined conditions, for each speed and load, of engine control inputs, including at least fueling mass flow rate, injection timing (FI), spark timing (SI) and exhaust recompression obtained by negative valve overlap (NVO). During load change rates below a predetermined threshold, SI, FI and NVO change rates are synchronized to current changes in the fueling mass flow rate. For fast load increases above the threshold, the cylinder charge is temporarily enriched by increasing the percentage of residual gas or reducing the percentage of fresh air mass in the charge sufficiently to maintain auto-ignition temperature during the load change. This may be done by delaying NVO action for a predetermined speed-dependent number of engine cycles. At very low loads, stable fuel rate reduction may require an alternate method involving deceleration fuel cut-off followed by a step change during refire.