Eight molecular dynamics simulations of a hydrated lipid bilayer have been carried out differing only in the applied surface tension, gamma, defining the boundary conditions of the periodic cell. The calculated surface area per molecule and deuterium order parameter profile are found to depend strongly on gamma. We present several methods to calculate the area compressibility modulus, K-A, from the simulations. Equivalence between the constant area and constant surface tension ensembles is investigated by comparing the present simulations with earlier work from our laboratories and we find simulation results to depend much more strongly on the specified surface area or surface tension than on the ensemble employed.