We use prior and boundary estimates as the approximation of outside probability and establish our beam thresholding strategies based on these estimates. Lexical items, e.g. head word and head tag, are also incorporated to lexicalized prior and boundary estimates. Experiments on the Penn Chinese Treebank show that beam thresholding with lexicalized prior works much better than that with unlexicalized prior. Differentiating completed edges from incomplete edges paves the way for using boundary estimates in the edge-based beam chart parsing. The beam thresholding based on lexicalized prior, combined with unlexicalized boundary, runs faster than that only with lexicalized prior by a