The original flash sintering experiment was carried out by applying an electric field, and switching to current control at the onset of the flash, signaled by a rise in conductivity. Here, we consider experiments where the experiment is controlled from the very start, by injecting current, which is increased at a constant rate. The current rates are varied from 50 mA/min to 5000 mA/min. The experiment is continued until, in all cases, the current density reaches 100 mA/mm(2). The total duration of the experiment ranged from approximately 7 seconds to 700 seconds. The following comparisons to the earlier voltage-to-current experiments are noted: (a) in both instances, the onset of the flash is signaled by an unusual rise in conductivity; however, since the power supply remains in the current control mode, the increase in conductivity is manifested by a drop in the voltage generated across the specimen; (b) the blackbody radiation model is modified to include the energy absorbed in specific heat, in order to determine the time-dependent change in temperature as the current is increased-this correction is particularly significant at the very high current rates; (c) sintering occurs continuously, reaching full density, in all instances, when the current density reaches similar to 100 mA/mm(2); and (d) these early experiments suggest that the current-rate experiments yield fine-grained microstructure across the entire gauge section of the dog-bone specimen, presumably because the highly transient conditions of voltage-to-current flash experiments are sidestepped. The experiments were carried out on 3 mol% yttria-stabilized zirconia.