A method implemented by computer for optimizing the cruising trajectory of an aircraft comprises the steps consisting in receiving the parameters of a reference trajectory, the trajectory comprising one or more plateaus and the transitions between these plateaus, the transitions being ascending or descending; and determining, in response to a request received in the course of the flight, at least one candidate alternative trajectory; and determining one or more indicators associated with the candidate alternative trajectory such as determined. Developments comprise the optional display of at least one indicator, indicators associated with the fuel consumption, with a difference in flight time or with the operational cost of the flight of the aircraft, the use of ratios of indicators, the inhibition of descending transitions, particular plateau length transitions as well as economical modes of transition. System aspects are described, comprising avionic or non-avionic means.