The main result of this paper, built on previous work by the author and T. Wilson, is the proof that the theory “ADR+DC + there is an R-complete measure on Θ” is equiconsistent with “ZF+DC+ ADR + there is a supercompact measure on ℘ω1(℘(R))+Θ is regular.” The result and techniques presented here contribute to the general program of descriptive inner model theory and in particular, to the general study of compactness phenomena in the context of ZF+DC.