The problem of whether a stellarator configuration can be made insensitive to the plasma pressure by using an external vertical magnetic field as a control parameter is discussed. Conventional stellarators with a planar circular axis are analysed. It is shown that for these systems the condition of Pfirsch-Schluter current suppression can be formulated as a two dimensional equation with all quantities expressed in terms of the vacuum magnetic field only. The major advantage of this formulation is that it allows the problem to be solved without solving the equilibrium equations. The formulation is used as a basis for showing that complete suppression of the Pfirsch-Schluter current by means of the vertical field is possible, in principle, both in shear free systems and in stellarators with l ⩾ 3. In l=2 stellarators with shear it is possible to obtain significant reduction of the current and to suppress the pressure induced plasma column shift. This phenomenon may be called `integral independence` of beta in contrast to true local independence in other cases. In all cases, a large inward shift of the plasma column is necessary, which is outside the operational range in all existing devices except Heliotron-E. In recent experiments in Heliotron-E, the state of being `integrally` independent of beta was almost fully achieved. The present study was stimulated by this result