Microstability properties of the Tormac sheath are discussed with particular emphasis on the influence of strong inhomogeneities and magnetic shear on the lower‐hybrid‐drift and mirror‐drift‐cone instabilities. It is found that magnetic shear can completely stabilize the lower‐hybrid‐drift instability (Maxwellian ions), and lead to a reduction in growth rate of the mirror‐drift‐cone instability (loss‐cone ions). The persistence of the mirror‐drift‐cone instability (at a reduced growth rate) in the presence of moderate magnetic shear suggests that the addition of a cold plasma component (as in the 2X‐IIB mirror experiment) may be desirable to further reduce the instability growth rate and suppress the associated anomalous transport.