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In this paper we explore whether a general topology network built up of routers with very small buffers, can maintain high throughput under TCP's congestion control mechanism. Recent results on buffer sizing challenged the widely used assumption that routers should buffer millions of packets. These new results suggest that when smooth TCP traffic goes through a single tiny buffer of size O(log W), then close-to-peak throughput can be achieved; W is the maximum window size of TCP flows. In this work, we want to know if a network of many routers can perform well when all buffers in the network are made very small, independent of the structure of the network. This scenario represents a real network where packets go through several buffering stages on their routes. Assuming the ingress TCP traffic to a network is paced, we first prove that all routers can get by with very small buffers, if the network has a tree structure. For networks with general topology, we propose a simple active queue management policy called bounded jitter policy (BJP), and show that under the proposed policy each flow will preserve its smooth pattern across the network. Logarithmic size buffers would therefore be enough in every router of the network.