The effects of magnetic shear on the drift instability, driven by a density gradient, are investigated. Both the collisional and the collisionless regimes are considered and it is found that in many cases this instability is of convective type, propagating away from the point where k·B = 0. Stability conditions are derived, showing that in the collisional regime the amount of shear necessary to stabilize the drift mode is generally less than that required to stabilize the resistive normal mode driven by unfavourable magnetic curvature. Since a less severe condition is instead obtained for the modes driven by a favourable magnetic curvature, an indication in favour of minimum-B toroidal systems is deduced. In the collisionless regime only moderate amounts of shear are required to completely stabilize the convective density-gradient drift mode.