This paper presents a method for speeding up a deep parser through backbone extraction and pruning based on CFG ambiguity packing. The TRIPS grammar is a wide-coverage grammar for deep natural language understanding in dialogue, utilized in 6 different application domains, and with high coverage and sentence-level accuracy on human-human task-oriented dialogue corpora (Dzikovska, 2004). The TRIPS parser uses a best-first beam search algorithm and a chart size limit, both of which are a form of pruning focused on finding an n-best list of interpretations. However, for longer sentences limiting the chart size results in failed parses, while increasing the chart size limits significantly impacts the parsing speed.