If a laser- or particle beam-driven plasma wakefield accelerator operates in the linear or moderately nonlinear regime, injecting an externally produced particle bunch (witness) to be accelerated may encounter an alignment problem. Witness alignment tolerances can be relaxed by using a damper, an additional particle bunch produced by the same injector and propagating at a submillimeter distance ahead of the witness. If misaligned, the damper perturbs the wakefield in such a way that the witness shifts on-axis with no quality loss.