This paper describes an algorithm for computing optimal structural descriptions for Optimality Theory grammars with context-free position structures. This algorithm extends Tesar's dynamic programming approach (Tesar, 1994) (Tesar, 1995@ to computing optimal structural descriptions from regular to context-free structures. The generalization to contextfree structures creates several complications, all of which are overcome without compromising the core dynamic programming approach. The resulting algorithm has a time complexity cubic in the length of the input, and is applicable to grammars with universal constraints that exhibit context-free locality. .
