Abstract. Previous work have assumed an independent model for overlay networks: a graph with independent link capacities. We introduce a model of overlays (LCC-overlay) which incorporates correlated link capacities by formulating shared bottlenecks as linear capacity constraints. We define metrics to measure overlay quality. We show that LCC-overlay is perfectly accurate and hence enjoys much better quality than the inaccurate independent overlay. We discover that even the restricted node-based LCC yields significantly better quality. We study two problems in the context of LCC-graphs: widest-path and maximum-flow. We also outline a distributed algorithm to efficiently construct an LCC-overlay.