Molecular dynamics simulations of a model bilayer in a solvent are used to determine the structure factors S(q) and other correlations at vanishing lateral tension of the system and at positive and negative tensions as well. The role played by curvature in the absence of surface tension, metastability, and phase transitions, and the dependence on the specific area, are discussed. Possible height-height correlation functions S(q) are examined and tested. (C) 2004 American Institute of Physics.