Discs of finite size are a very rare form of stable surfactant self-assembly. It is shown that mixing of two oppositely charged single-chain surfactants can produce rigid nanodiscs as well as swollen lamellar liquid crystals with frozen bilayers. The crucial requirement for obtaining nanodisc self-assembly is the use of H+ and OH- as counterions. These counterions then form water and lower the conductivity to 10 microsiemens per centimeter. In the case of cationic component excess, a dilute solution of nanodiscs is in thermodynamic equilibrium with a lamellar phase. The diameter of the cationic nanodiscs is continuously adjustable from a few micrometers to 30 nanometers, with the positive charge located mainly around the edges.