Electron motion in a single electrostatic wave in a sheared magnetic field is shown to become stochastic in the presence of a second wave at an amplitude well below that obtained from the overlapping pendulum resonance approximation. The enhanced stochasticity occurs for low parallel velocity electrons for which the parallel trapping motion fromeE∥/minteracts strongly with theE×Btrapping motion due to the presence of magnetic shear. The single‐wave particle motion is given by a two‐parameter family of one‐degree‐of‐freedom Hamiltonians which bifurcate from a pendulum phase space to a topology with three chains of elliptic and hyperbolic fixed points separated in radius about the mode‐rational surface. In the presence of a perturbing wave with a different helicity, electrons in the small parallel velocity regime become stochastic at an amplitude scaling as the fourth root of the wave potential. The results obtained for stochastic motion apply directly to the problem of the diffusion of electrons in drift waves.