A method is described that is implemented by computer for optimizing the vertical descent profile of an aircraft, the vertical profile being broken down into an altitude profile and a speed profile. One or more altitudes of passage can be determined by minimizing the overall deviation between the speed profile and one or more speed constraints previously received. The optimized descent profile can comprise one or more of these altitudes of passage. Different developments are described, in particular embodiments in which an optimized altitude of passage minimizes the engine thrust, the descent profile is of OPEN IDLE, FPA or VS type, the optimized descent profile is determined backward, a speed constraint is of AT or AT OR ABOVE type, and the use of the airbrakes. Display modalities are described, as are system and software aspects.