A major limitation of current unstructured peer-topeer (P2P) networks lies in the inefficiency of search, which results in fatal scalability problems. In this paper, ToA^3, a novel P2P file-sharing system, is proposed to tackle such a limitation. The key idea of ToA^3 is to generate an overlay topology with DESIRABLE properties, adapt peers towards BETTER neighbors dynamically, and direct queries to RIGHT next nodes with as few duplicated messages as possible. To achieve this goal, ToA^3 introduces several innovative techniques such as: (a) a dynamic topology adaptation algorithm with self-sustaining power-law degree distributions, (b) a simply but efficient utilization of peerto- peer network heterogeneity, (c) a proper implementation of the underlying-network-awareness, and (d) Smart Search-a biased search algorithm used in ToA^3. Extensive simulations substantiate that our techniques significantly improve the search performance and reduce the network load dramatically.