Submicron magnetite crystals with mean sizes of 0.037, 0.10 and 0.22 Wm undergo major changes in hysteresis properties and domain states in crossing the Verwey transition (T V W120 K). The 0.037 Wm crystals are single-domain (SD) both in the cubic phase at room temperature T 0 and in the monoclinic phase below T V . The 0.10 and 0.22 Wm crystals have a mixture of SD and two-domain (2D) states at room temperature T 0 , but mainly SD structures below T V , in agreement with micromagnetic calculations. Coercive force H c increases on cooling through T V , by a factor 3^5 in the submicron magnetites and 40 in a 1.3 mm single crystal, because of the high crystalline anisotropy and magnetostriction of monoclinic magnetite. As a result, domain walls and SD moments are so effectively pinned below T V that all remanence variations in warming or cooling are reversible. However, between W100 K and T 0 , remanence behavior is variable. Saturation remanence (SIRM) produced in monoclinic magnetite at 5 K drops by 70^100% in warming across T V , with minor recovery in cooling back through T V (ultimate levels at 5 K of 23^37% for the submicron crystals and 3% for the 1.3 mm crystal). In contrast, SIRM produced in the cubic phase at 300 K decreases 5^35% (submicron) or s 95% (1.3 mm) during cooling from 300 to 120 K due to continuous re-equilibration of domain walls, but there is little further change in cooling through T V itself. However, the submicron magnetites lose a further 51 5% of their remanence when reheated through T V . These irreversible changes in cycling across T V , and the amounts of the changes, have potential value in determining submicron magnetite grain sizes. The irreversibility is mainly caused by 2DCSD transformations on cooling through T V , which preserve or enhance remanence, while SDC2D transformations on warming through T V cause remanence to demagnetize. ß