Locating entities in peer-to-peer environments is a fundamentaloperation. Recent studies show that the concept of distributed hash table can be used to design scalable lookup schemes with good performance (i.e. small routing table and lookup length). In this paper, we propose a simple framework for deriving decentralized lookup algorithms. The proposed framework is simple in that it is based on the well-known concept of k-ary search. To demonstrate the applicability of our framework, we show how it can be used to instantiate Chord. When deriving a generalized Chord from our framework, we obtain better performance in terms of the routing table size (38% smaller than the generalization suggested by the Chord authors).