An apparatus is disclosed that includes a memory controller chip and memory chips packaged with the memory controller chip. Each memory chip includes normal-retention storage rows that exhibit retention times greater or equal to a first time interval, and having been tested to generate information identifying low-retention storage rows that exhibit retention times less than the first time interval. Refresh logic refreshes the normal-retention storage rows at a first refresh rate corresponding to the first time interval, and refreshes each low-retention storage row at a second refresh rate that is greater than the first refresh rate.