Context. Uranus’s bulk composition remains unknown. Although there are clear indications that Uranus’s interior is not fully convec-tive, and therefore has a non-adiabatic temperature profile, many interior models continue to assume an adiabatic interior. Aims. In this paper we present a new method for interpreting empirical structure models in terms of composition and for identifying non-convective regions. We also explore how the uncertainty in Uranus’s rotation period and winds affects the inferred composition and temperature profile. Methods. We used Uranus’s density profiles from previous work in which the density is represented by up to three polytropes. Results. Using our new method, we find that these empirical models imply that Uranus’s interior includes non-adiabatic regions. This leads to significantly hotter internal temperatures, which can reach several tens of thousands of kelvins, and higher bulk heavy-element abundances (up to 1 M_⊕) compared to standard adiabatic models. We find that the assumed rotation period strongly affects the inferred composition, while the winds have a negligible effect. Although solutions with only H–He and rock are possible, we find that the maximum water-to-rock ratio in Uranus for our models ranges between 2.6 and 21. This is significantly lower compared to standard adiabatic models. Conclusions. We conclude that it is important to include non-adiabatic regions in Uranus structure models as they significantly affect the inferred temperature profile and, therefore, the inferred bulk heavy-element abundance. In addition, we suggest that to decrease the uncertainty in Uranus’s bulk composition, it is of great value to measure Uranus’s gravitational field and determine its rotation period.