The series of experiments carried out in recent years on the HBTX reversed field pinch [Plasma Phys. Controlled Fusion 30, 843 ( 1988)] have highlighted the importance of minimizing the flux that penetrates the plasma-wall boundary. This flux penetration, whether from equilibrium field errors, the presence of limiters, or plasma magnetic activity from the growth of thin shell modes, leads to an increase in the loop voltage. The magnitude of this increase can be understood in terms of magnetic helicity balance. Feedback stabilization of the (m,n) = ( 1,2) thin shell mode has been successfully demonstrated, though with little effect on global plasma properties. A new design is being developed for HBTX aimed at minimizing the flux that can penetrate the' first wall.