As pointed out earlier, the pion–quark interaction based on a bag model with a sharp, fixed surface gives rise to the divergence of various quantities such as the nucleon self-energy. This is due to quark excitation in the intermediate states. We examine how this difficulty can be moderated in a "fuzzy bag model" in which the surface is smeared. The nucleon self-energy due to pion interaction converges in the fuzzy bag model. We find, however, that the convergence is quite slow, and the contribution of processes such as [Formula: see text] pair creation, which have not been considered in earlier calculations, is very important.