  Although the complex Langevin method can solve the sign problem in
simulations of theories with complex actions, the method will yield the wrong
results if known validity conditions are not satisfied. We present a novel
method to compute observables for a target ensemble by reweighting complex
trajectories generated with the complex Langevin method for an auxiliary
ensemble having itself a complex action. While it is imperative that the
validity conditions be satisfied for the auxiliary ensemble, there are no such
requirements for the target ensemble. This allows us to enlarge the
applicability range of the complex Langevin method. We illustrate this at the
hand of a one-dimensional partition function and two-dimensional
strong-coupling QCD.
