Uranus' bulk composition remains unknown. Although there are clear indications that Uranus' interior is not fully convective, and therefore has a non-adiabatic temperature profile, many interior models continue to assume an adiabatic interior. In this paper we present a new method to interpret empirical structure models in terms of composition and for identifying non-convective regions. We also explore how the uncertainty in Uranus' rotation period and winds affect the inferred composition and temperature profile. We use Uranus' density profiles from previous work where the density is represented by up to three polytropes. Using our new method, we find that these empirical models imply that the interior of Uranus includes non-adiabatic regions. This leads to significantly hotter internal temperatures that can reach a few 10^3^K and higher bulk heavy-element abundances (up to 1 Earth-mass) 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 ratio in Uranus for our models ranges between 2.6 and 21. This is water-to-rock significantly lower compared to standard adiabatic models. 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 it is of great value to measure Uranus' gravitational field and determine its rotation period in order to decrease the uncertainty in Uranus' bulk composition.