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While the ability to simulate nondeterminism and compute multiple solutions for a single query is a powerful and attractive feature of logic programming languages, it is expensive in both time and space. Since programs in such languages are very often functional, i.e. do not produce more than one distinct solution for a single input, this overhead is especially undesirable. This paper describes how programs may be analyzed statically to determine which literals and predicates are functional, and how the program may then be optimized using this information. Our notion of ``functionality'' subsumes the notion of ``determinacy'' that has been considered by various researchers. Our algorithm is less reliant on language features such as the cut, and thus extends more easily to parallel execution strategies, than others that have been proposed.