  Nontopological solitons, or ``bags,'' can arise when fermions acquire their
mass through a Yukawa coupling to some scalar field. Bags have played an
important role in models of baryons, nuclei, and more recently, in the idea
that a Higgs condensate may form around a very heavy top quark. It has been
claimed that deep bags, which correspond to tightly-bound states of fermions,
will form when the Yukawa coupling is strong. Quantum corrections, however, are
significant in this regime. We examine the effects of these quantum corrections
on the formation of nontopological solitons in an exactly solvable large-$N$
model. We find that quantum bags differ dramatically from those of the
classical theory. In particular, for large Yukawa coupling, the bags remain
shallow and the fermions weakly bound.
