Monte Carlo (MC) lattice simulation studies have been performed for a compressible polymer melt over a wide range of cohesion energies or densities. The free surface of the melt was examined with respect to its concentration profile, surface thickness D, and surface tension sigma. For various reduced intersegmental energies, e (e < 0), we found that sigma is proportional to -e1/2 and that D varies linearly with (e(c) - e)-1/2, where e(c) is a critical value of the reduced intersegmental energy; both relations are analogous to those for a polymer-polymer interface. The surface thickness for a representative system was calculated to be in the range D almost-equal-to 1.5-4.0 nm. Relative to the values found with the equation-of-state theory for surface tension of Sanchez and Poser and with the functional integral approach of Hong and Noolandi, we observed somewhat lower densities and thicker interfaces for given cohesion energies. The observed surface profiles are also symmetric rather than asymmetric as predicted by these theories. Our equation for the dimensionless parameter sigma(red) versus T(red) provides realistic values for the surface tension and its temperature coefficient using parameters obtained from data for the bulk polymers. The microscopic analysis of the interface from the MC simulation results revealed a surface enrichment by chain ends, a layering of coil centers beneath the surface, a continuous variation in intersegmental contacts, and a strong deformation of coils in the interface. We also found a slight variation of coil dimensions in the bulk for different temperatures and cohesion energies.