It is well known that D-dimensional vacuum gravity with D-2 commuting Killing vectors is integrable. For such theories a solution generating technique has been available since it was first presented by Belinski and Zakharov in 1978. This method, which was later improved by Pomeransky, and has been successfully used to construct new black hole solutions, as well as to re-derive previously known solutions. In this talk I will first show how this method can be applied to five-dimensional minimal supergravity. In the second part I will describe how it can be employed in six dimensions to generate dipole black rings in a five-dimensional Einstein-Maxwell-dilaton theory.