  We develop the diagrammatic technique of quiver subtraction to facilitate the
identification and evaluation of the $\mathrm{SU}(n)$ hyper-K\"ahler quotient
(HKQ) of the Coulomb branch of a $3d$ $\mathcal{N}=4$ unitary quiver theory.
The target quivers are drawn from a wide range of theories, typically
classified as ''good'' or ''ugly'', which satisfy identified selection
criteria. Our subtraction procedure uses quotient quivers that are ''bad'',
differing thereby from quiver subtractions based on Kraft-Procesi transitions.
The procedure identifies one or more resultant quivers, the union of whose
Coulomb branches corresponds to the desired HKQ. Examples include quivers whose
Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits
of classical and exceptional type, and slices in the affine Grassmanian. We
calculate the Hilbert Series and Highest Weight Generating functions for HKQ
examples of low rank. For certain families of quivers, we are able to
conjecture HWGs for arbitrary rank. We examine the commutation relations
between quotient quiver subtraction and other diagrammatic techniques, such as
Kraft-Procesi transitions, quiver folding, and discrete quotients.
