Structural properties of a finite number (N=2−20) of point charges (classical electrons) confined laterally in a two-dimensional two-minima potential are calculated as a function of the distance (d) between the minima. The particles are confined by identical parabolic potentials and repel each other through a Coulomb potential. Both ground-state and metastable electron configurations are discussed. Discontinuous transitions from one configuration to another as a function of d are observed for N=6, 8, 11, 16, 17, 18, and 19. We show that the structural transitions have quantum-mechanical counterparts also in the limit of noninteracting electrons. ; Peer reviewed