A quark bag model for nucleons and isobars is made with pions existing only outside the bag. The pion field is introduced so as to ensure continuity of the axial-vector current at the boundary of the bag. It is argued that the bag can be quite small, of radius ∼ħ/ mnc where mn is the nucleon mass. The energy of the small bag is much larger than mnc 2, but self-energy processes, especially those involving the pion, are invoked in order to bring the nucleon energy down to its physical value. The resulting theory looks very much like the old Yukawa theory for a pion with a small distributed source, the source now being described in terms of quarks.