A read operation for selected memory cell on a selected word line compensates for program disturb which is a nonlinear function of the data state of an adjacent memory cell on an adjacent word line. When a command to perform a read operation for the selected memory cell is received, a read operation is first performed on the adjacent memory cell to determine its data state, or to classify the adjacent memory cell into a threshold voltage range which includes one or more data states, or a portion of a data state. The selected memory cell is then read using a baseline control gate voltage which does not provide compensation, and one or more elevated control gate voltages which provide compensation, to distinguish between two adjacent data states. An optimal sensing result is selected based on the data state or threshold voltage range of the adjacent memory cell.