The well-known ‘displace, cut and reflect’ method used to generate discs from given solutions of Einstein field equations is applied to the superposition of two extreme Reissner–Nordström black holes to construct discs made of charged dust and also non-axisymmetric planar distributions of charged dust on the z = 0 plane. They are symmetric with respect to two or one coordinate axes, depending on whether the black holes have equal or unequal masses, respectively. For these non-axisymmetric distributions of matter we also study the effective potential for geodesic motion of neutral test particles.