  In this paper we consider the moduli space of complete, conformally flat
metrics on a sphere with k punctures having constant positive Q-curvature and
positive scalar curvature. Previous work has shown that such metrics admit an
asymptotic expansion near each puncture, allowing one to define an asymptotic
necksize of each singular point. We prove that any set in the moduli space such
that the distances between distinct punctures and the asymptotic necksizes all
remain bounded away from zero is sequentially compact, mirroring a theorem of
D. Pollack about singular Yamabe metrics. Along the way we define a radial
Pohozaev invariant at each puncture and refine some a priori bounds of the
conformal factor, which may be of independent interest.
