A phenomenological viscosity model for steady-state flows of non-Newtonian polymeric fluids has been proposed based on the assumption of uniqueness of viscosity. The separable dependences of viscosity on the second and third invariants of the rate of deformation tensor represent the key ingredient of the model, i.e. eta = eta(SH)(II(d))Tr(III(d)). The model fits experimental data of shear and extensional viscosities of various polymer melts and solutions. These data show shear-thinning, extension-thinning, extension-thickening, and extension-thickening with a maximum (and a minimum). The application of the viscosity model in numerical simulation of contraction flow predicts non-monotonically increasing vortex enhancement, which is in agreement with experiments. The third invariant dependence of viscosity which, in the current work, is not introduced merely to give a large Trouton ratio, is discussed. It is found that the third invariant can vary significantly between an unadulterated extensional flow and an adulterated one, a fact which can affect viscosity dramatically.