A parsing makes 1-best search efficient by suppressing unlikely 1-best items. Existing kbest extraction methods can efficiently search for top derivations, but only after an exhaustive 1-best pass. We present a unified algorithm for k-best A parsing which preserves the efficiency of k-best extraction while giving the speed-ups of A methods. Our algorithm produces optimal k-best parses under the same conditions required for optimality in a 1-best A parser. Empirically, optimal k-best lists can be extracted significantly faster than with other approaches, over a range of grammar types.