The most important rheological and mathematical features of the pom-pom model are presently used to compare and improve other constitutive models such as the Giesekus and Phan-Thien-Tanner models. A pragmatic methodology is selected that allows derivation of simple constitutive equations, which are suited to possible software implementation. Alterations to the double convected pom-pom, Phan-Thien-Tanner and Giesekus models are proposed and assessed in rheometric flows by comparing model predictions to experimental data.