A spark-ignition supercharged internal-combustion gasoline engine is equipped with a system for variable actuation of the intake valves including a pressurized fluid chamber set between intake valve and a respective control cam, and an electrically actuated valve, the opening of which vents the pressure chamber so as to cause rapid closing of the valve, as a result of the respective elastic return means, even when the respective cam would tend to keep the valve open. The variable-valve-actuation system is used in combination with control cams of the intake valves shaped in such a way as to generate an intake valve lift profile including a boot portion with substantially constant lift. The boot portion is provided in the final part of the opening cycle of the intake valve, after bottom dead center.