Method and apparatus for use with multi-bank Synchronous Dynamic Random Access Memory (SDRAM) circuits, modules, and memory systems are disclosed. In one described embodiment, an SDRAM circuit receives a bank address to be used in an auto-refresh operation, and performs the auto-refresh operation on the specified bank and for a current refresh row. The device is allowed to enter a self-refresh mode before auto-refresh operations have been completed for all banks and the current refresh row. The memory device completes refresh operations for the current refresh row before proceeding to perform self-refresh operations for new rows. Other embodiments are described and claimed.