It has been shown that the minimum-energy state of a diffuse pinch discharge is that described by the so-called 'Bessel Function Model'. The structure of this state is related to a limiting case of the 'Tangled Discharge Model', and it is shown that random currents normal to the magnetic field will prevent the attainment of this state unless the conductivity is large (in the strict sense, infinite). Estimates of the minimum-conductivity required are given.