A re-programmable non-volatile memory system, such as a flash EEPROM system, having its memory cells grouped into blocks of cells that are simultaneously erasable is operated to perform memory system housekeeping operations in the foreground during execution of a host command, wherein the housekeeping operations are unrelated to execution of the host command. Both one or more such housekeeping operations and execution of the host command are performed within a time budget established for executing that particular command. One such command is to write data being received to the memory. One such housekeeping operation is to level out the wear of the individual blocks that accumulates through repetitive erasing and re-programming.