Magnetites with sizes from 1 ¿m to 135 ¿m were cooled in zero field and their magnetizations M(T) measured continuously. M(T) changed reversibly in cooling from T0 = 300 K to 200 K, and in subsidiary warming-cooling cycles Ti → T0 → Ti for any Ti. Changes in M(T) in cooling from 200 K to 130 K were largely irreversible due to decreasing magnetocrystalline anisotropy which promotes wall unpinning and domain nucleation. Low-temperature demagnetization (LTD) is almost complete by 130 K in 20--135 ¿m magnetites but in 1--14 ¿m magnetites further LTD occurs on cooling to 120 K as magnetocrystalline easy axes change and domains reorganize at the Verwey transition. The observed irreversible changes are the basis of stepwise LTD as a method of paleomagnetic cleaning. Decrements ΔM in remanence due to cooling are most accurately measured at T0, requiring a set of warming-cooling cycles Ti → T0 → Ti. A less accurate method, continuous LTD, measures decrements M(Ti) - M(Ti-1) from the main cooling curve below 200 K, without intermediate warming-cooling cycles; this requires remanence measurements at Ti < T0. Stepwise or continuous LTD curves M(Ti) discriminate among remanence types and grain sizes. The signal of finer (PSD) grains is enhanced compared to coarser (MD) grains. Analogous to the Lowrie and Fuller <1971> test, the inverse thermoremanence (ITRM) of 1--14 ¿m grains is harder to stepwise LTD than saturation remanence (SIRM), while anhysteretic remanence (ARM) is harder than either; for 20--135 ¿m multidomain grains, ITRM is softer than SIRM.