Recent approaches to English-language sentence compression rely on parallel corpora consisting of sentence-compression pairs. However, a sentence may be shortened in many different ways, which each might be suited to the needs of a particular application. Therefore, in this work, we collect and model crowdsourced judgements of the acceptability of many possible sentence shortenings. We then show how a model of such judgements can be used to support a flexible approach to the compression task. We release our model and dataset for future work.