The circuit and method of this invention provide for rapid and reliable detection of depleted or nearly-depleted cells in a column. The circuit is formed on the substrate of a nonvolatile, integrated-circuit memory including rows and columns of memory cells. The drain of each memory cell is connected to a drain-column line and the control gate that is connected to a wordline. One input of a sense amplifier is connected to the drain-column line. The other input of the sense amplifier is connected to a current reference formed on said substrate. The wordline is connected to a wordline test voltage and the output of the sense amplifier is coupled to an output pin of the integrated circuit. The current through the drain-column line is compared with the current through the current reference and, if the current through the drain-column line is sufficiently close to the current through said current reference, a signal is transmitted to an output pin of the integrated circuit.