Each of a plurality of flash memory cells is programmed to a respective one of L.gtoreq.2 threshold voltage states within a threshold voltage window. A histogram is constructed by determining how many of some or all of the cells have threshold voltages in each of two or more of m.gtoreq.2 threshold voltage intervals within the threshold voltage window. Reference voltages for reading the cells are selected based on estimated values of shape parameters of the histogram. Alternatively, the cells are read relative to reference voltages that define m.gtoreq.2 threshold voltage intervals that span the threshold voltage window, to determine numbers of at least a portion of the cells whose threshold voltages are in each of two or more of the threshold voltage intervals. Respective threshold voltage states are assigned to the cells based on the numbers without re-reading the cells.