A IRCRAFT trajectory optimization is a subject of great importance in air traffic management from the point of view of defining optimal flight procedures that lead to energy-efficient flights. In practice, the airlines consider a cost index (CI) and define the direct operating cost (DOC) as the combined cost of fuel consumed and flight time weighted by the CI. Their goal is to minimize the DOC. However, in the presence of unexpected winds, the flight timemay differ considerably from the scheduled time, which leads to an arrival-error cost that can be added to the DOC to obtain the total cost (TC). Minimum-DOC trajectories have been studied by different authors [1–6]. The related problem of minimum fuel with fixed final time has been analyzed as a minimum-DOC problem with free final time in [3,5,7] (the problem is to find the time cost for which the corresponding free final time DOC-optimal trajectory arrives at the assigned time); this same problem is addressed in [8], analyzing the effects of mismodeled winds in a scenario formed by the final cruise and descent segments. The problem of minimum-cost flight, considering not only the DOC but also the arrival-error cost, is analyzed in [9,10], taking into account factors such as crew overtime cost, passenger dissatisfaction cost, and losses due to missed connections. In this Note, the problem of minimum-cost cruise at constant altitude in the presence of strong winds, including the arrival-error cost, is analyzed, considering the general unsteady problem, with variable aircraft mass, and without any restriction on cruise altitude. The main objective is to analyze the optimal trajectories that lead to minimum cost, defined as optimal speed laws (speed as a function of aircraft mass). The analysis is made using the theory of singular optimal control (see [11]), which has the great advantage of providing feedback control laws (control variables as functions of the state variables) that can be directly used to guide the aircraft along the optimal path. These optimal control laws are analyzed as well. In this work, the initial and final speeds are given, so that the optimal control is of the bang-singular-bang type, and the optimal paths are formed by a singular arc and two minimum/maximumthrust arcs joining the singular arc with the given initial and final points (see [6,12]). In previous work related to optimum cruise at constant altitude [13,14], only the singular arc was studied; hence, a more general formulation of the optimal problem is addressed now, apart from considering the arrival-error cost and including wind effects (average horizontal winds). In this analysis of the minimum-TC problem, the arrival-error cost depends on the difference between the actual and the scheduledflight times, and it is defined to be positive, so that both late and early arrivals are penalized (the objective is to achieve high arrival-time accuracy). It will be shown that, for some values of the parameters of the problem, minimum cost is obtained when the final time coincides with the scheduled time of arrival; that is, when the arrival-error cost is zero. This critical case is in fact a problem with fixed final time. Results are presented for a model of a Boeing 767-300ER.