A multi-cylinder internal-combustion engine, comprising: at least one intake valve and at least one exhaust valve for each cylinder, each provided with respective elastic return means that bias the valve into a closed position, for controlling the respective intake and exhaust conduits, at least one camshaft, for actuating the intake valves and the exhaust valves of the engine cylinders by means of respective tappets, wherein at least each intake valve is a valve with variable actuation, being controlled by a respective tappet against the action of the aforesaid elastic return means, by interposition of hydraulic means including a pressurized fluid chamber, facing which is a pumping piston connected to the tappet of the valve, said pressurized fluid chamber (c) being configured to be connected by means of an electrically actuated valve to a discharge channel in order to uncouple the valve with variable-actuation from the respective tappet and cause rapid closure of the valve as a result of the respective elastic return means, electronic control means for controlling each electrically actuated valve in such a way as to vary the time and the extension of the opening of the variable-actuation valves as a function of one or more operating parameters of the engine, wherein the control cam of each intake valve is shaped in such a way as to generate a valve-lift profile that includes a boot portion with substantially constant lift, wherein said boot portion with substantially constant lift is provided in the final part of the lift cycle of the intake valve and terminates after BDC, and wherein said electronic control means are configured for controlling said electrically actuated valve so that said boot portion with substantially constant lift is reduced in duration by opening the electrically actuated valve when it is required to operate with a shorter closure delay of the intake valves, the engine being characterized in that it is a spark-ignition engine, in particular a supercharged spark-ignition engine, preferably a gasoline engine, and in that the ratio between said constant lift (H, b) of the boot portion and a maximum lift (a) of the intake valve is comprised between 0.5 and 1. at least one intake valve and at least one exhaust valve for each cylinder, each provided with respective elastic return means that bias the valve into a closed position, for controlling the respective intake and exhaust conduits, at least one camshaft, for actuating the intake valves and the exhaust valves of the engine cylinders by means of respective tappets, wherein at least each intake valve is a valve with variable actuation, being controlled by a respective tappet against the action of the aforesaid elastic return means, by interposition of hydraulic means including a pressurized fluid chamber, facing which is a pumping piston connected to the tappet of the valve, said pressurized fluid chamber (c) being configured to be connected by means of an electrically actuated valve to a discharge channel in order to uncouple the valve with variable-actuation from the respective tappet and cause rapid closure of the valve as a result of the respective elastic return means, electronic control means for controlling each electrically actuated valve in such a way as to vary the time and the extension of the opening of the variable-actuation valves as a function of one or more operating parameters of the engine, wherein the control cam of each intake valve is shaped in such a way as to generate a valve-lift profile that includes a boot portion with substantially constant lift, wherein said boot portion with substantially constant lift is provided in the final part of the lift cycle of the intake valve and terminates after BDC, and wherein said electronic control means are configured for controlling said electrically actuated valve so that said boot portion with substantially constant lift is reduced in duration by opening the electrically actuated valve when it is required to operate with a shorter closure delay of the intake valves, the engine being characterized in that it is a spark-ignition engine, in particular a supercharged spark-ignition engine, preferably a gasoline engine, and in that the ratio between said constant lift (H, b) of the boot portion and a maximum lift (a) of the intake valve is comprised between 0.5 and 1.