A frequent challenge in applications that use entities extracted from text documents is selecting the most salient entities when only a small number can be used by the application (e.g., displayed to a user). Solving this challenge is particularly difficult in the setting of extremely short documents, such as the response from a digital assistant, where traditional signals of salience such as position and frequency are less likely to be useful. In this paper, we propose a lightweight and data-efficient approach for entity salience detection on short text documents. Our experiments show that our approach achieves competitive performance with respect to complex state-of-the-art models, such as GPT-4, at a significant advantage in latency and cost. In limited data settings, we show that a semi-supervised fine-tuning process can improve performance further. Furthermore, we introduce a novel human-labeled dataset for evaluating entity salience on short question-answer pair documents.