Internet routers require buffers to hold packets during times of congestion. The buffers need to be fast, and so ideally they should be small enough to use fast memory technologies such as SRAM or all-optical buffering. Unfortunately, a widely used rule-of-thumb says we need a bandwidth-delay product of buffering at each router so as not to lose link utilization. This can be prohibitively large. In a recent paper, Appenzeller et al. challenged this rule-of-thumb and showed that for a backbone network, the buffer size can be divided by N without sacrificing throughput, where N is the number of flows sharing the bottleneck. In this paper, we explore how buffers in the backbone can be significantly reduced even more, to as little as a few dozen packets, if we are willing to sacrifice a small amount of link capacity. We argue that if the TCP sources are not overly bursty, then fewer than twenty packet buffers are sufficient for high throughput. Specifically, we argue that O(log W) buffer...