A 3N-parameter (3 parameters per mode) phenomenological modification of the XPP model for a description of the rheological properties of polymer melts is proposed. The predictive/fitting capabilities of the modified XPP model are compared with the Giesekus, XPP, and modified Leonov models using various polymeric materials in steady shear and uniaxial elongational flows. Its predictability of the rheological properties of the studied materials seems to be very good, including strain hardening in uniaxial elongational flow. Consequently, the GS derivative term was implemented into this modified XPP model. Then the model contains two linear parameters per mode (relaxation time and shear modulus) and two non-linear ones (the fitting parameter simultaneously controlling both strain hardening in elongation flow and shear thinning, and the slip parameter influencing almost solely shear thinning). The efficiency of this model is tested using LDPE and HDPE materials and compared with the modified Leonov model and network-based exponential PTT and PTT-XPP models, both of them containing the GS derivative term.