The application of cyclic stress to a ferromagnet normally gives irreversible magnetization shifts towards the anhysteretic magnetization. Here experimental measurements are presented that show the irreversible magnetization changes induced by cyclic uniaxial isofield stress applied after magnetization at particular points on minor hysteresis loops. Selecting the (M,H) point and magnetization history, then applying stress cycles of increasing amplitude enables irreversible changes, initially away from and later toward the anhysteretic curve, to be obtained. Examples of a second inversion (i.e., irreversible shifts initially toward, then away and subsequently toward the anhysteretic magnetization) with increasing amplitude cyclic uniaxial stress are also given. Preisach diagrams are used to interpret these results qualitatively in terms of local, more extensive and global anhysteretic states.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>