A closed packed system ("onion phase") of so-called lamellar droplets, consisting of concentric surfactant bilayers which are separated from one another by water, may be obtained by subjecting a continuous lamellar phase to shear. We propose a model for the size of these lamellar droplets under shear as a function of their effective surface tension. This model fits the available experimental data quantitatively and explains the dependence of the size on surfactant volume fraction.