The equilibrium structure of closed self-avoiding tethered vesicles are investigated by molecular dynamics simulations. To allow for local flexibility, the vesicles are constructed by connecting lineax chains of n monomers to form a closed membrane. For all n studied, 0 ≤n ≤16, we find that the membranes remain flat. The height fluctuations ⟨h2⟩∼Nζ, where ζ = 0.55 ± 0.02 and N is the total number of monomers in the vesicle. This result for ζ is significantly lower than earlier estimates for open membranes with a free perimeter but is in agreement with recent estimates of Abraham for membranes without a free perimeter. Results for the static structure factor, S(q), are calculated and compared to recent data on red blood cell skeletons.