A method optimizing fuel-injection control with driving speeds of apparatuses adjusted by controlling a turbine speed according to power, and optimizing control of a free turbine power package of an aircraft, including a low-pressure body, supplying power to apparatuses and linked to a high-pressure body. The method varies the low-pressure body speed to obtain a minimum speed for the high-pressure body, so power supplied by the apparatuses remains constant. Power supplied by the apparatuses is dependent upon the apparatuses driven speed by the low-pressure body, and a speed set point of the low-pressure body is dependent upon a maximum value of minimum speeds of the apparatuses, enabling required power to be optimized, upon a positive or zero incrementation added to the speed set point of the low-pressure body to minimize speed of the high-pressure body to the apparatuses power supply.