We investigated the influence of hydrostatic and nonhydrostatic stress on the recording process of magnetic field intensity with particular relevance for meteorites that experienced pressures lower than 5 GPa corresponding to the lowest shock stage classification (S1) in meteorites. Thermal remanent magnetizations were imparted on natural obsidian samples containing pseudo-single domain titanomagnetite, analogous to some achondritic meteorites. Thellier-type paleointensity experiments were carried out at ambient conditions after pressure cycling to 0.6, 1.2, and 1.8 GPa. Each experiment used 10 samples to assess reproducibility, which is better than ±5%. The recorded paleointensity decreased 10%/GPa under hydrostatic stress and 20%/GPa under nonhydrostatic stress, leading to the fundamental conclusion that paleointensity results from meteorites may be appreciably underestimated. Pressure cycling shifts the blocking and unblocking spectra, thereby producing more linear slopes on an Arai diagram with increasing strain. We explain why, for samples with a single magnetization component that does not alter, a two-step paleointensity protocol sufficiently resolves the true paleointensity. Moreover, we propose that pressure cycling of pseudo-single domain bearing samples will remove the inherent curvature of the Arai slope, thereby allowing one to obtain a more accurate estimate of the true paleointensity. This likely also holds true for samples possessing multidomain grains. Conversely, linear trends on Arai plots in meteorites might have their origin in a pressure effect that does not necessarily reflect the ubiquitous presence of single domain particles.