A DRAM memory device includes several banks of memory cells each of which are divided into first and second sets of memory cells. The memory cells in the first set can be refreshed at a relatively slow rate to reduce the power consumed by the DRAM device. Error checking and correcting circuitry in the DRAM device corrects any data retention errors in the first set of memory cells caused by the relatively slow refresh rate. The memory cells in the second set are refreshed at a normal rate, which is fast enough that data retention errors do not occur. A mode register in the DRAM device may be programmed to select the size of the second set of memory cells.