Lipid bilayers are simulated using flexible simulation cells in order to allow for relaxations in area per lipid as bilayer content and temperature are varied. We develop a suite of Monte Carlo (MC) moves designed to generate constant surface tension γ and constant pressure P and find that the NPT partition function proposed by Attard [J. Chem. Phys.1995, 103, 9884-9885] leads to an NPγT partition function with a form invariant to choice of independent shape variables. We then compare this suite of MC moves to NPγT MC moves previously employed in our group as well as a pair of MC moves designed to replicate the NP aP aT "ensemble" often used in molecular dynamics simulations to yield zero surface tension and constant pressure. A detailed analysis of shape fluctuations in a small bilayer system reveals that the two latter MC move sets are different from one another as well as from our new suite of MC moves, as justified by careful analysis of the partition functions. However, the study of a larger bilayer system reveals that, for practical purposes for this system, all six MC move sets are comparable to one another. © 2012 American Chemical Society.