Changes in the impedance, ≊600%/Oe, at axial fields less than 1 Oe have been observed in the presence of a 90 kHz, few mA current through a soft, nearly zero magnetostrictive wire. In this 125 μm diameter CoFeSiB amorphous wire we observe a total change of 160% at the maxima of the impedance in dc fields less than 2 Oe. A systematic study of the role of induced anisotropy in the axial, circumferential, and helical directions on the magneto‐impedance shows that the largest effect is seen in the wire annealed to obtain circumferential easy axis using a 15 mA ac current passing through it. Both the axial hysteresis loops and the observed I‐V characteristics reflect the induced anisotropies. The observed dependence of the inductance change on the type of the anisotropy induced in these wires can be modeled in terms of an interplay between the induced anisotropy, reversing ac field, and the axial dc field.