With the help of the energ y principle in tokamaks, a class of perturbations is studied, which, if unstable, cannot be stabilized by the toroidal main field. On the assumption of usual tokamak ordering and in the limit of infinite aspect ratio, these perturbations are shown to be minimizing among all axisymmetric perturbations. In the case of finite aspect ratio, a detailed stability analysis is carried out by using a constant-pressure surface-current model with elliptic, triangular or rectangular plasma cross-section. Definite stabilization by toroidal effects and by ßp is demonstrated.