I will present a technique called “quotient quiver subtraction” which, in physics language, gauges subgroups of Coulomb branch global symmetries. The action on the Coulomb branch is a hyper-Kähler quotient. I will demonstrate the features of this algorithm with many examples, mostly drawn from Coulomb branch constructions of nilpotent orbit closures. Along the way we will encounter new relationships between nilpotent orbit closures and other varieties such as Slodowy slices and affine Grassmannian slices, including those of exceptional type. These examples may be viewed as an extension of the work of Kostant-Brylinski and Kobak-Swann to actions on nilpotent orbit closures by non-Abelian continuous groups.