  We study wall-crossing phenomena in the McKay correspondence. Craw-Ishii show
that every projective crepant resolution of a Gorenstein abelian quotient
singularity arises as a moduli space of $\theta$-stable representations of the
McKay quiver. The stability condition $\theta$ moves in a vector space with a
chamber decomposition in which (some) wall-crossings capture flops between
different crepant resolutions. We investigate where chambers for certain
resolutions with Hilbert scheme-like moduli interpretations - iterated Hilbert
schemes, or 'Hilb of Hilb' - sit relative to the principal chamber defining the
usual $G$-Hilbert scheme. We survey relevant aspects of wall-crossing, pose our
main conjecture, prove it for some examples and special cases, and discuss
connections to other parts of the McKay correspondence.
