A large fraction of the experimental efforts searching for the (QCD) axion focus on smaller-scale resonant searches, making the axion mass one of the key quantities. In theory, the axion mass can be inferred from the observed dark matter abundance and numerical simulations point towards an axion mass (slightly) higher than currently searched for. These numerical studies require axion models to have both high quality and a predictive cosmological history - that is - a post-inflationary scenario. In this talk, I want to introduce the minimal requirements to obtain axions with exponentially good quality and a predictive cosmological scenario. These ingredients appear in theories where an axion coming from a higher-form gauge field mixes with the phase of a complex scalar field. We present a simple toy model on a 5-dimensional manifold with boundary. If time permits, we show how these scenarios may arise in string theory compactifications and discuss how to overcome additional complications these specific UV completions introduce.
