This study addresses entropic segregation effects at the surfaces of monodisperse and bidisperse melts. For the monodisperse melts, we focus on the segregation of chain ends to the surface, and for the bidisperse melts, we examine the segregation of short polymers to the surface. Universal shapes have been predicted for their concentration profiles, but the derivations rely on the mean-field approximation, which only treats the excluded-volume interactions in an approximate manner. To test whether or not the predictions hold up when the polymers are rigorously prevented from overlapping, we compare mean-field calculations with Monte Carlo simulations performed on the exact same model. Apart from a significant increase in the statistical segment length, the rigorous enforcement of excluded-volume interactions has a relatively small effect on the mean-field predictions. In particular, the universal profiles predicted by mean-field theory are found to be accurate.