We systematically investigate solutions of a modified Lee-Friedberg model for fermions bound in a non-linearly self-interacting scalar field o-. In this model a running a-fermion coupling strength g(a) is introduced such as to interpolate between a perturbative vacuum with a=0 and a non-trivial vacuum (a=o-~) with strong coupling. We find soliton-bag-like solutions in which the fermions experience absolute confinement. These solutions are almost independent of the detailed form of g(a).