The temperature dependence of coercive force H-c was studied on well-characterized and stoichiometric millimetre-sized single crystals of magnetite at a series of 16 temperatures from 300 to 10 K using a SQUID magnetometer. H-c decreases gradually with cooling to the isotropic temperature, T-i = 130 K, where the first magnetocrystalline anisotropy constant K-1 becomes zero. H-c exhibits a sharp increase at the Verwey transition, T-v = 120 K, where the structure changes from cubic to monoclinic. In crossing the Verwey transition, H-c increases by more than two orders of magnitude, from 20 mu T to 2.4 mT, and the shape of the hysteresis loops becomes wasp-waisted. Observed coercivity between 300 K and 170 K varies with temperature as lambda(s) /M-s , where lambda(s) is the magnetostriction constant and M-s is the saturation magnetization, indicating that the coercivity in MD magnetite is controlled mainly by internal stress associated with dislocations or other crystal defects. It seems likely that the stable single-domain-like magnetic memory observed in large MD magnetite crystals is due to magnetoelastically pinned domain walls. The discontinuous change in H-c at the Verwey transition is controlled by abrupt changes in magnetocrystalline and magnetostriction constants due to crystal deformation from cubic to monoclinic structure.