Recent advances in language modeling have enabled new conversational systems. In particular, it is often desirable for people to make choices among specified options when using such systems. We address the problem of reference resolution, when people use natural expressions to choose between real world entities. For example, given the choice `Should we make a Simnel cake or a Pandan cake?` a natural response from a non-expert may be indirect: `let's make the green one`. Reference resolution has been little studied with natural expressions, thus robustly understanding such language has large potential for improving naturalness in dialog, recommendation, and search systems. We create AltEntities (Alternative Entities), a new public dataset of entity pairs and utterances, and develop models for the disambiguation problem. Consisting of 42K indirect referring expressions across three domains, it enables for the first time the study of how large language models can be adapted to this task. We find they achieve 82\%-87\% accuracy in realistic settings, which while reasonable also invites further advances.