A method for data storage includes defining at least first and second read commands for reading storage values from analog memory cells. The first read command reads the storage values at a first accuracy, and the second read command reads the storage values at a second accuracy, which is finer than the first accuracy. A condition is evaluated with respect to a read operation that is to be performed over a given group of the memory cells. One of the first and second read commands is selected responsively to the evaluated condition. The storage values are read from the given group of the memory cells using the selected read command.