  We show the existence of bound two-electron states in an almost depleted
two-dimensional island. These two-electron states are carried by special
compact configurations of four single-electron levels. The existence of these
states does not require phonon mediation, and is facilitated by the
disorder-induced potential relief and by the electron-electron repulsion only.
The density of two-electron states is estimated and their evolution with the
magnetic field is discussed.
