  We study the structure of Brownian loop-soup clusters in two dimensions.
Among other things, we obtain the following decomposition of the clusters with
critical intensity: When one conditions a loop-soup cluster by its outer
boundary $\gamma$ (which is known to be an SLE(4)-type loop), then the union of
all excursions away from $\gamma$ by all the Brownian loops in the loop-soup
that touch $\gamma$ is distributed exactly like the union of all excursions of
a Poisson point process of Brownian excursions in the domain enclosed by
$\gamma$. A related result that we derive and use is that the couplings of the
Gaussian Free Field (GFF) with CLE(4) via level-lines (by Miller-Sheffield), of
the square of the GFF with loop-soups via occupation times (by Le Jan), and of
the CLE(4) with loop-soups via loop-soup clusters (by Sheffield and Werner) can
be made to coincide. An instrumental role in our proof of this fact is played
by Lupu's description of CLE(4) as limits of discrete loop-soup clusters.
