A memory system includes logical banks divided into sub-banks or collections of sub-banks. The memory system responds to memory-access requests (e.g., read and write) directed to a given logical bank by sequentially accessing sub-banks or collections of sub-banks. Sequential access reduces the impact of power-supply spikes induced by memory operations, and thus facilitates improved system performance. Some embodiments of the memory system combine sequential sub-bank access with other performance-enhancing features, such as wider power buses or increased bypass capacitance, to further enhance performance.