Sources responsible for volcanic unrest produce characteristic surface deformation. Given a sufficient number of distributed observation points, inversion is the preferred procedure for retrieving the source parameters of location and volume or pressure change. Most often the solutions have been for point sources embedded in a homogeneous half-space. Recent work indicates that layered structures, particularly those with soft superficial layers, significantly perturb the deformation pattern compared with that for the homogeneous medium. We apply the methods of L. Crescentini and A. Amoruso to data for the most recent mini-uplift in the Campi Flegrei caldera and show that models using a homogeneous medium cannot adequately fit all the data. Incorporating a layered structure appropriate for Campi Flegrei allows a significantly better fit, avoiding characteristic discrepancies which are revealed by a synthetic test. Failure to use such structure results in incorrect source parameters, possibly leading to misleading geophysical interpretations.