We compare the FENE and FENE-P models in different flow situations. We start with Brownian dynamics simulations of start-up of shear and uniaxial elongational flow. The FENE-P model predicts the FENE behaviour unsatisfactorily. However, we will show that its performance can be substantially improved. We propose to determine the parameters in the FENE-P model such that important FENE flow characteristics are recovered. The three resulting models (FENE, FENE-P and the proposed FENE-P model) will first be compared in the above-mentioned rheometrical flows. To show that the improvement persists in a complex flow field, we also simulate the flow of the FENE fluid past a cylinder using the Brownian configuration field technique. We then compare the results with those of the proposed FENE-P model and those of the original FENE-P model.