  We find solutions to the 1+1 dimensional scalar-only linear sigma model. A
new method is used to compute 1-fermion loop contributions exactly and
agreement with published results employing other methods is excellent. A
renormalization scheme which differs from that commonly used in such
calculations but similar to that required in 1+3 dimensions is also presented.
We compare ``kink'' {\it versus} ``shallow bag'' solutions paying careful
attention to the implications of the 1-fermion loop contributions for the
stability of the former. We find that, for small fermion multiplicities,
self-consistent shallow bag solutions are always more bound than their
metastable kink counterparts. However, as the fermion multiplicity increases,
shallow bags evolve into kinks which eventually are the only self-consistent
configurations. This situation is qualitatively the same for the two
renormalization schemes considered. When we construct ``baryons'', each
containing three fermions, the kink configuration is typically more bound than
the shallow bag when 1-fermion loop contributions are included.
