The effort for determining NMR interaction tensors from orientation-dependent spectra of single crystals may be greatly reduced by exploiting symmetry relations between atoms of the observed nuclide in the unit cell, as is well documented in the literature. In this work, we determined both the full chemical shift (CS) tensor of 207Pb and the unknown orientation of the rotation axis for the natural mineral phosgenite, Pb2Cl2CO3, from a single rotation pattern, i.e. spectra of crystal orientations from 0 to 180°. In the tetragonal crystal structure of phosgenite, four symmetry-related, but magnetically inequivalent 207Pb are generated by the Wyckoff multiplicity. The mineral wulfenite, PbMoO4, also crystallises in a tetragonal space group, but the site multiplicity for 207Pb generates only one magnetically inequivalent atom, thus not supplying sufficient experimental data to determine CS tensor and axis orientation from an arbitrary number of rotation patterns. One solution to this problem is to simultaneously acquire data of a known compound with high symmetry and Wyckoff multiplicity (here: phosgenite), which supplies additional constraints making the solution of the target compound (here: wulfenite) possible. The 207Pb CS tensors thus determined are characterised by the following eigenvalues in ppm: δ11PAS=(−2553±1), δ22PAS=(−1929±1), δ33PAS=(−1301±1) for phosgenite, and δ11PAS=(−2074±1), δ22PAS=(−2074±1), δ33PAS=(−1898±1) for wulfenite.