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In unstructured peer-to-peer (P2P) networks, the overlay topology (or connectivity graph) among peers is a crucial component in addition to the peer/data organization and search. Topological characteristics have profound impact on the efficiency of a search on such unstructured P2P networks, as well as other networks. A key limitation of scale-free (power-law) topologies is the high load (i.e., high degree) on a very few number of hub nodes. In a typical unstructured P2P network, peers are not willing to maintain high degrees/loads as they may not want to store a large number of entries for construction of the overlay topology. Therefore, to achieve fairness and practicality among all peers, hard cutoffs on the number of entries are imposed by the individual peers, which limits scale-freeness of the overall topology, hence limited scale-free networks. Thus, it is expected that the efficiency of the flooding search reduces as the size of the hard cutoff does. We investigate the construction of scale-free topologies with hard cutoffs (i.e., there are not any major hubs) and the effect of these hard cutoffs on the search efficiency. Interestingly, we observe that the efficiency of normalized flooding and random walk search algorithms increases as the hard cutoff decreases.