The software alignment of planar tracking detectors using samples of charged particle trajectories may lead to global detector distortions that affect vertex and momentum resolution. We present an alignment procedure that constrains such distortions by making use of samples of decay vertices reconstructed from two or more trajectories and putting constraints on their invariant mass. We illustrate the method by using a sample of invariant-mass constrained vertices from D-0 -> K-pi(+) decays to remove a curvature bias in the LHCb spectrometer. (c) 2013 Elsevier B.V. All rights reserved.