A method for operating a compression ignition engine includes forming a combustible mixture by mixing generally homogeneously a first fuel and air and introducing this mixture into the at least one cylinder, compressing the combustible mixture with the piston in a compression stroke, injecting a second fuel to the combustible mixture at an injection-time of the second fuel during the compression stroke but before start of combustion, and continuing the compression stroke until combustion starts at those locations in the at least one cylinder where concentration of the second fuel is highest and/or the temperature of the mixture is the highest. Emission of the cylinder and/or mechanical stress of the cylinder caused by the combustion are monitored, and if emissions and/or mechanical stress are above respective predetermined thresholds, individually for the cylinder, the amount and/or the timing of the second fuel injected, and/or temperature of the cylinder charge is changed, such that the emission of the cylinder and/or mechanical stress of the cylinder is decreased lower than the corresponding predetermined threshold.