  GLR* is a recently developed robust version of the Generalized LR Parser,
that can parse almost ANY input sentence by ignoring unrecognizable parts of
the sentence. On a given input sentence, the parser returns a collection of
parses that correspond to maximal, or close to maximal, parsable subsets of the
original input. This paper describes recent work on developing an integrated
heuristic scheme for selecting the parse that is deemed ``best'' from such a
collection. We describe the heuristic measures used and their combination
scheme. Preliminary results from experiments conducted on parsing speech
recognized spontaneous speech are also reported.
