Pseudocontact shifts (PCS) contain a wealth of geometric information, which makes paramagnetic NMR one of the best methods for accurate geometric determinations in solution. It is well-known that PCS are intrinsically linked to Fermi contact (FC) shifts, and the separation of the two terms is achieved through linearization methods, which heavily rely on (a) isostructurality (even concerning a labile axial site) and (b) the validity of Bleaney's constants. Recently we proposed a method that circumvents both assumptions in the case of axially symmetric complexes, and presently we generalize it to lower symmetry. Our method is model-free and thus does not rely on any structural hypothesis. Our results compare very well with recently published data obtained through an accurate ab initio approach.