The dependence of the differential cross-section for on-shell W-pair production on the anomalous trilinear gauge couplings invariant under C and P is examined. It is shown that the contributions of the anomalous magnetic moments of the W boson due to the photon and the Z can be individually projected out by means of two appropriately constructed polynomials. The remaining four anomalous couplings are shown to satisfy a set of model-independent sum rules. Specific models which predict special relations among the anomalous couplings are then studied; in particular, the composite model of Brodsky and Hiller, and the linear and non-linear effective Lagrangian approaches. The relations predicted by these models, when combined with the aforementioned sum rules, give rise to definite predictions, particular to each model. These predictions can be used, at least in principle, in order to exclude or constrain such models.