Low-temperature demagnetization (LTD), consisting of zero-field cycling from room temperature to 77 K and back to room temperature, was performed on magnetites from different sources having grain sizes between 0.037 μm and 5 mm. The memory fractions, RI and RT of saturation isothermal remanent magnetization (IRMs) and 0.1 mT thermoremanent magnetization (TRM), respectively, have a strong intrinsic grain-size dependence below ≈10 μm, but are almost size independent in the multidomain (MD) range above 10 μm. The size dependence of RI and RT in the MD range reported by Parry (1979, 1980) probably results from stress introduced during crushing to obtain finer size fractions. We demonstrate that the method of preparation of magnetites, irregularities in the crystals, and increase or decrease of the state of internal stress by quenching or annealing all have a direct effect on the amount of magnetic memory. Magnetic memories (the fractions of TRM and IRMs surviving after LTD) are much more resistant against alternative-field (AF) demagnetization than the original TRM and IRMs before LTD. Even large magnetite crystals (≫20 μm) reveal a hard, single-domain-like component of magnetization when the softer magnetization is removed by LTD. A comparison of AF demagnetization properties of IRMs and TRM in these MD magnetites shows that the Lowrie and Fuller (1971) test must be reinterpreted. ¿ American Geophysical Union 1992