A memory module can be programmed to deliver relatively wide, low-latency data in a first access mode, or to sacrifice some latency in return for a narrower data width, a narrower command width, or both, in a second access mode. The narrow, higher-latency mode requires fewer connections and traces. A controller can therefore support more modules, and thus increased system capacity. Programmable modules thus allow computer manufacturers to strike a desired balance between memory latency, capacity, and cost.