We report on magnetic properties and compositions of titanomaghemites from moderately to highly oxidized basalts recovered at nine drilling sites in the Pacific Ocean. These new data, together with similar data sets, allow us to test compositional fields of titanomaghemite that could carry self-reversed components of natural remanent magnetization above room temperature. These compositions have been proposed on the basis of theoretical considerations of cation distributions during ionic reordering associated with low-temperature oxidation (maghemitization). The data indicate that very high oxidation states (z ≥ 0.9) and relatively high Ti contents (x ≥ 0.6) are needed to produce natural self-reversed components; this compositional range is much more limited than predicted. The severe restrictions on compositions and oxidation state strongly suggest that self-reversed magnetizations should not be a general feature of the magnetization carried by oceanic basalt. Instead, the formation of self-reversed components may signify unusual conditions, such as extreme fluid flow and iron removal, which could result in the required oxidation states while maintaining stability of the cation-deficient titanomaghemite lattice structure.