We have magnetically characterized single crystal Fe3O4/NiO superlattices grown on MgO(001), where the layer thickness has been varied over a wide range. Hysteresis for modulation wavelength LAMBDA(mod) = 258 angstrom is similar to bulk Fe3O4, while loops for LAMBDA(mod) < 80 angstrom are nearly linear with applied field with minimal hysteresis and remanence. The magnetization slopes of the latter are roughly proportional to LAMBDA(mod), and increase from 5 to 300 K. MeasurementS above 300 K suggest that both exchange coupling across NiO/Fe3O4 interfaces and strain-induced variations in anisotropy, rather than paramagnetism, lead to this linear behavior.