We are interested in constructing machines which learn to understand and act upon fluently spoken input. For any particular task, certain linguistic events are critical to recognize correctly, others not so. This notion can be quantified via salience, which measures the information content of an event for a task. In previous papers, salient words have been exploited to learn the mapping from spoken input to machine action for several tasks. In this work, a new algorithm is presented which automatically acquires salient grammar fragments for a task, exploiting both linguistic and extra-linguistic information in the inference process. Experimental results will be reported for a database of fluently spoken customer requests to operators, responding to the open-ended prompt of ‘Hello, this is AT&T. How may I help you?’