This paper reports room temperature measurements of initial susceptibility &khgr;0, second Rayleigh coefficient B, coercive force Hc, remanent coercive force HR, and the ratio Jrs/Js of near-saturation remanent and induced magnetizations for four samples containing single-crystal magnetite cubes with mean sizes of 0.037, 0.076, 0.10, and 0.22 μm. While &khgr;0 and Hc have weak dependences on particle size d, Hc and Jrs vary strongly with size, as d-0.55 and d-0.75, respectively, over the 0.076-0.22 μm range. These hysteresis properties and their size dependences are incompatible with data for >1-μm crushed and annealed magnetite grains. Nearly perfect unstrained crystals tend to have Hc and Jrs values 2-5 times smaller than those of pulverized grains of nominally the same size. Magnitudes and size dependences of Hc and Jrs for >0.06-μm magnetites are approximately, although not perfectly, accounted for by (1) metastable single-domain (SD) particles, (2) rotatable SD-like domain wall (DW) moments, or (3) DW displacements impeded by crystal defects and limited by self-demagnetization. Only reversible DW displacements (or possibly domain rotations) opposed by self-demagnetization can explain the initial susceptibility data, however.