A method for operating a combustion engine after a cold start, the combustion engine including a supercharger device, a plurality of combustion chambers, a fuel-injection device injecting into each of the combustion chambers, and a gas-exchange valve control device that controls gas-exchange valves in a variable manner. A rich fuel-air mixture is generated in the combustion chambers, and the combustion-chamber charges are ignited in a retarded manner. Following the cold start, the combustion engine is operated with first valve overlaps that are greater than in a warm combustion engine. A first exhaust valve of a first combustion chamber is initially closed at such a late point that its opening duration overlaps with the opening duration of a second exhaust valve of a second combustion chamber that directly follows the first combustion chamber in the ignition sequence and that discharges into the same exhaust manifold as the first combustion chamber.