We construct a compactification $M^{\mu ss}$ of the Uhlenbeck-Donaldson type
for the moduli space of slope stable framed bundles. This is a kind of a moduli
space of slope semistable framed sheaves. We show that there exists a
projective morphism $\gamma \colon M^s \to M^{\mu ss}$, where $M^s$ is the
moduli space of S-equivalence classes of Gieseker-semistable framed sheaves.
The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows
one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli
spaces of framed ideal instantons.