[en] Bag models of hadrons inspired by quantum chromodynamics have a problem in that it is difficult to realize the hard-core repulsion between nucleons without corrections, and the nucleon collapses. We include into the color dielectric model pions, effects of one-gluon exchange and a center-of-mass correction, and investigate how they contribute to the repulsive core by comparing masses of a three-quark bag and of a six-quark bag. Results of numerical calculations show that to make the nucleon stable without zero-point energy one has to take a weak coupling for pions, which suggests a cloudy-bag-like picture rather than a chiral-bag-like one. If, however, one prefers the latter picture which is in better agreement with physical observables in this model, one then has to include the zero-point energy in some way. (orig.)