Perturbation-theory techniques are used to generate an approximate transcendental equation for the leading Regge pole produced by an infinite sum of Feynman ladder diagrams. This equation is not restricted to the weak-coupling domain and can be used to produce trajectories with α(0)>0 . The equation is solved both below and above the elastic and inelastic thresholds to provide the first complete description of a relativistic Regge trajectory in the ladder-diagram model. The same technique is used to generate potential-theory trajectories which agree with the exact solutions obtained by more complicated methods.