We introduce two new optimization models for the aircraft conflict avoidance problem that aims at issuing decisions on both speed and heading-angle deviations to keep aircraft pairwise separated by a given separation distance. The first model is a new mixed-integer nonlinear formulation. The second model is a continuous optimization formulation, less typical in aircraft conflict avoidance. The advantages of the two models are combined within a three-phase method that we propose to solve the problem to global optimality. Computational experiments on various instances from the literature yield very promising results, and show the effectiveness of the proposed models and of the three-phase solution approach.