The simultaneous presence of tearing modes of different helical pitches leads to the destruction of magnetic surfaces, which has been suggested as the mechanism leading to the onset of the disruptive instability in tokamaks. For current profiles in which them=2 mode is unstable, but them=3 is stable, the coupling of them=3 to them=2 through the poloidal variation of the toroidal field can drive them=3 amplitude &psgr;3to order &psgr;2times the inverse aspect ratio. Detailed calculations, including nonlinear effects, have been performed for two models for the equilibrium andm=2 mode structure. A slab model and incompressiblem=3 perturbations are assumed. Them=3 amplitude increases with shear, up to a point, showing that as the current channel shrinks, overlap of resonances becomes more likely. Our results also apply qualitatively to otherm,m±1 interactions.