  We show how to construct a resolution of symplectic orbifolds obtained as
quotients of presymplectic manifolds with a torus action. As a corollary, this
allows us to desingularise generic symplectic quotients. Given a manifold with
a Hamiltonian action of a compact Lie group, symplectic reduction at a
coadjoint orbit which is transverse to the moment map produces a symplectic
orbifold. If moreover the points of this coadjoint orbit are regular elements
of the Lie coalgebra, that is, their stabiliser is a maximal torus, the result
for torus quotients may be applied to obtain a desingularisation of these
symplectic orbifolds. Regular elements of the Lie coalgebra are generic in the
sense that the singular strata have codimension at least three.
  Additionally, we show that even though the result of a symplectic cut is an
orbifold, it can be modified in an arbitrarily small neighbourhood of the cut
hypersurface to obtain a smooth symplectic manifold.
