It is well known that the saturation magnetostriction in nearly nonmagnetostrictive amorphous ribbons decreases with applied stress at a typical rate of 10-10 MPa-1. In this report we show by means of a simple experiment that a similar behavior is observed in samples constructed by piling up ribbons with high magnetostriction and opposite sign. A simple calculation points out that the strength of the stress dependence is governed by fluctuations in. It is concluded that zero magnetostriction may be reasonably achieved in Co-rich metallic glasses as a result of the coexistence of different magnetostrictive phases.