The freezing transition of tensionless fluctuating vesicles is investigated by Monte Carlo simulations and scaling arguments for a simple tether-and-bead model of fluid membranes. In this model, a freezing transition is induced by reducing the tether length. In the case of planar membranes (with periodic boundary conditions), the model shows a fluid-to-crystalline transition at a tether length ℓ0≃(1.53±0.01)σ0, where σ0 is the bead diameter. For flexible vesicles with bending rigidities $0.85k_{\rm B}T\leq k\leq \sqrt{3}k_{\rm B}T$, the reduced free energy of dislocations with Burgers vector 〈ℓ〉,Fdloc/k, is found to scale for small tether lengths with the scaling variable k/(K0〈ℓ〉2), where K0 is the Young modulus of a crystalline membrane of the same tether length, and 〈ℓ〉 is the average nearest-neighbor distance. This is a strong indication that free dislocations are present, so that the membrane is in a hexatic phase for small tether lengths. A hexatic-to-fluid transition occurs with increasing tether length. With decreasing bending rigidity, this transition moves to smaller tether lengths.