It has been suggested that the recently observed fast sawtooth crashes are caused by a low‐shear, pressure‐driven ideal instability. This hypothesis is investigated, using asymptotic methods to solve the toroidal mode equations for a class of equilibria characterized by a low‐shear central region in whichq−1 is small, separated from the wall by a region with finite shear. A dispersion relation that differs significantly from previous results is obtained. An explicit expression for the growth rate is given for a modelqprofile.