This paper addresses the efficient processing of top-k queries in wide-area distributed data repositories where the index lists for the attribute values (or text terms) of a query are distributed across a number of data peers and the computational costs include network latency, bandwidth consumption, and local peer work. We present KLEE, a novel algorithmic framework for distributed top-k queries, designed for high performance and flexibility. KLEE makes a strong case for approximate top-k algorithms over widely distributed data sources. It shows how great gains in efficiency can be enjoyed at low result-quality penalties. Further, KLEE affords the query-initiating peer the flexibility to trade-off result quality and expected performance and to trade-off the number of communication phases engaged during query execution versus network bandwidth performance. We have implemented KLEE and related algorithms and conducted a comprehensive performance evaluation. Our evaluation employed real-world and synthetic large, web-data collections, and query benchmarks. Our experimental results show that KLEE can achieve major performance gains in terms of network bandwidth, query response times, and much lighter peer loads, all with small errors in result precision and other result-quality measures