The general coupled tearing-mode dispersion relation is investigated in tokamaks. A differential rotation of rational surfaces in high temperature devices is found to decouple low amplitude modes, so that they only reconnect magnetic flux at one surface in the plasma and behave ideally at the remaining surfaces. Above a threshold mode amplitude, the rational surfaces start to lock together, permitting modes to develop which simultaneously reconnect magnetic flux at more than one surface. Such modes are generally more unstable than uncoupled modes. Ideal rational surfaces, on which there is no reconnection, located close to the plasma edge are found to shield free-boundary tearing modes from the destabilizing influence of external-kink modes. The threshold mode amplitude required to lock coupled rational surfaces decreases rapidly with increasing machine dimensions