The linear resistive-MHD layer equations are solved numerically for the internal kink mode and the dispersion relation is obtained. The author considers two rather unorthodox types of q(r) profile, both of which have zero shear at the layer; i.e. (i) non-monotonic q(r) with a minimum value lying just above unity, (ii) monotonic q(r) with a point of inflection at q=1. One interesting feature of the author's results for both types of q(r) profile is the appearance of overstable solutions for certain parameter ranges. For class (i), the author finds that the mode becomes first overstable and then purely growing as the minimum value of q(r) decreases. For realistic plasma parameters the band of overstability is thin, but non-negligible. For class (ii), the author finds that for realistic plasma parameters the mode is completely stable.