Effective program synthesis requires a way to minimise the number of candidate programs being searched. A type signature, for example, places some small restrictions on the structure of potential candidates. We introduce and motivate a distilled program synthesis problem where a type signature is the only machine-readable information available, but does not sufficiently minimise the search space. To address this, we develop a system of property relations that can be used to flexibly encode and query information that was not previously available to the synthesiser. Our experience using these tools has been positive: by encoding simple properties and by using a minimal set of synthesis primitives, we have been able to synthesise complex programs in novel contexts.