  Motivated by Nekrasov's instanton counting, we discuss a method for
calculating equivariant volumes of non-compact quotients in symplectic and
hyper-K\"ahler geometry by means of the Jeffrey-Kirwan residue-formula of
non-abelian localization. In order to overcome the non-compactness, we use
varying symplectic cuts to reduce the problem to a compact setting, and study
what happens in the limit that recovers the original problem. We implement this
method for the ADHM construction of the moduli spaces of framed Yang-Mills
instantons on $\R^{4}$ and rederive the formulas for the equivariant volumes
obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated
residues of a single rational function.
