The injection system has a pump for supplying high-pressure fuel to a storage volume for supplying a number of injectors. The pump has at least one reciprocating pumping element performing a compression stroke synchronously with each fuel injection. The injection system has at least one control device for controlling the amount of fuel supplied by the pump to the storage volume, and which is controlled by a chopper control unit to modulate the fuel volume introduced into the compression chamber during the intake stroke (Ps-Pi). The delivery start instant of the pumping element during the compression stroke being unequivocally defined by the fuel volume introduced.