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Overlay network topology together with peer/data organization and search algorithm are the crucial components of unstructured peer-to-peer (P2P) networks as they directly affect the efficiency of search on such networks. Scale-free (power-law) overlay network topologies are among structures that offer high performance for these networks. A key problem for these topologies is the existence of hubs, nodes with high connectivity. Yet, the peers in a typical unstructured P2P network may not be willing or able to cope with such high connectivity and its associated load. Therefore, some hard cutoffs are often imposed on the number of edges that each peer can have, restricting feasible overlays to limited or truncated scale-free networks. In this paper, we analyze the growth of such limited scale-free networks and propose two different algorithms for constructing perfect scale-free overlay network topologies at each instance of such growth. Our algorithms allow the user to define the desired scale-free exponent ( γ). They also induce low communication overhead when network grows from one size to another. Using extensive simulations, we demonstrate that these algorithms indeed generate perfect scale free networks (at each step of network growth) that provide better search efficiency in various search algorithms than the networks generated by the existing solutions.