Cells of a flash memory are read by determining respective adaptive reference voltages for the cells and comparing the cells' threshold voltages to their respective reference voltages. The adaptive reference voltages are determined either from analog measurements of the threshold voltages of the cells' neighbors or from preliminary estimates of the cells' threshold voltages based on comparisons of the cells' threshold voltages with integral or fractional reference voltages common to all the cells. Cells of a flash memory also are read by comparing the cells' threshold voltages to integral reference voltages, comparing the threshold voltages of cells that share a common bit pattern to a fractional reference voltage, and adjusting the reference voltages in accordance with the comparisons.