A computer system includes a memory controller coupled to a memory module containing several DRAMs. The memory module also includes a non-volatile memory storing row addresses identifying rows containing DRAM memory cells that are likely to lose data during normal refresh of the memory cells. Upon power-up, the data from the non-volatile memory are transferred to a comparator in the memory controller. The comparator compares the row addresses to row addresses from a refresh shadow counter that identify the rows in the DRAMs being refreshed. When a row of memory cells is being refreshed that is located one-half of the rows away from a row that is likely to loose data, the memory controller causes the row that is likely to loose data to be refreshed. The memory controller also includes error checking circuitry for identifying the rows of memory cells that are likely to lose data during refresh.