This paper presents a pronoun resolution algorithm that adheres to the constraints and rules of Centering Theory (Grosz et al., 1995) and is an alternative to Brennan et al.'s 1987 algorithm. The advantages of this new model, the Left-Right Centering Algorithm (LRC), lie in its incremental processing of utterances and in its low computational overhead. The algorithm is compared with three other pronoun resolution methods: Hobbs' syntax-based algorithm, Strube's S-list approach, and the BFP Centering algorithm. All four methods were implemented in a system and tested on an annotated subset of the Treebank corpus consisting of 2026 pronouns. The noteworthy results were that Hobbs and LRC performed the best.