Abstract In this study we use micromagnetic modeling to show that the magnetizations of magnetically single‐vortex particles rotate toward the stress axis on the application of a differential compression stress. This is the exact opposite response to magnetically single‐domain particles, which previously provided the theoretical underpinning of the effect of stress on the magnetic signals of rocks. We show that the magnetization directions of single‐vortex and equant single‐domain particles are altered by much lower stresses than previously predicted, c.f., 100 versus 1,000 MPa; where a change in magnetization is defined as a rotation of >3° after the removal of stress. The magnetization intensity of assemblages also drops by ∼20%–30% on the application and removal of stress of ∼100 MPa. Given that single‐vortex particles are now thought to dominate the magnetization of most rocks, future studies should account for paleomagnetic directional uncertainties and potential underestimation of the ancient magnetic field intensity.