The adoption of voice assistants like Alexa or Siri has grown rapidly, allowing users instant access to information via voice search. Query suggestion is a standard feature of screen-based search experiences, allowing users to explore additional topics. However, this is not trivial to implement in voice-based settings. To enable this, we tackle the novel task of suggesting uestions with compact and natural voice hints to allow users to ask follow-up questions. We first define the task of composing speech-based hints, ground it in syntactic theory, and outline linguistic desiderata for spoken hints. We propose a sequence-to-sequence approach to generate spoken hints from a list of questions. Using a new dataset of 6, 681 input questions and human written hints, we evaluate models with automatic metrics and human evaluation. Results show that a naive approach of concatenating suggested questions creates poor voice hints. Our most sophisticated approach applies a linguistically-motivated pretraining task and was strongly preferred by humans for producing the most natural hints.