NMR spectra of many systems governed by axially symmetric second rank tensor interactions exhibit P2(cos θ) dependence on the angle 9 between the symmetry axis and the externally applied magnetic field. For the so-called "powder samples" consisting of many randomly oriented domains the resulting spectrum is the superposition of contributions from each such domain. This study deals with a numerical technique enabling one to obtain the lineshapes of such individual contributions responsible for the given powder spectrum. The electric dipolar interaction between two spin 1/2 nuclei produces a characteristic powder lineshape called "Pake doublet", after G.E.Pake, hence the name "de-pake-ing". An iterative algorithm capable of dealing with spectra produced by a variety of systems is developed and checked by applying it to a wide range of simulated NMR spectra. A set of characteristic "signatures" associated with different experimental situations is established and the limits of the applicability of the technique are determined.