The famous Gelfand duality lies at the heart of C*-algebra theory and much work over the past 80 years has been devoted to finding the best possible non-commutative extension.  Here we unify two of the more well-known non-commutative variants due to Dauns-Hofmann (1969) and Kumjian-Renault (1986/2008), resulting in a duality between strongly saturated Fell bundles over locally compact Hausdorff étale groupoids and C*-algebras carrying some extra Cartan-like structure.  Our approach is, however, quite different to its predecessors, being based on an ultrafilter construction inspired by classic topological results of Stone, Wallman and Milgram, as well as the more recent non-commutative Stone duality of Lawson.