(1) The sonication procedure of preparation of small unilamellar vesicles is modelled as a process of uniform random fragmentation of the lipid aggregates. The vesicle size distribution evolving in this process is shown to be identical with the Weibull extremal probability distribution. (2) Size histograms of sonicated small vesicles of various phospholipid composition were obtained by using electron microscopy (negative staining). Their successful simulation with Weibull curves shows that theory agrees with experiment. A similarly good agreement is found also with size histograms obtained by freeze-fracture of phosphatidylcholine-cholesterol vesicles (Van Venetië, R., Leunissen-Bijvelt, J., Verkleij, A.J. and Ververgaert, P.H.J.T.(1980) J. Microsc. 118, 401–408). This analysis allows a refinement of some earlier conclusions about the effect of cholesterol on the size of the sonicated vesicles. (3) It follows from the theoretical model that the only intrinsic characteristic of the sonicated vesicles is the lower limit of their size. The other characteristics of the size distribution such as expectancy, dispersion, position and height of the maximum depend on the intensity of fragmentation. (4) It is concluded that the size distribution of sonicated small vesicles is completely determined by the procedure of their preparation and, therefore, the condition of thermodynamic equilibrium between aggregated and monomeric lipid is irrelevant in this case.