The global ideal magnetohydrodynamic (MHD) stability of plasmas with a prescribed helical boundary deformation and nonvanishing toroidal current is investigated with respect to the (m,n) external modes with n = 1,2,3, and m = n + 1. L = 2, 3 and mixtures (of both) configurations were studied by systematically varying parameters such as the aspect ratio, the number of equilibrium field periods, the toroidal current density, and the pressure profiles. The study focuses mainly on the q < 2 area. It is shown that a fixed helical boundary deformation can stabilize the (m,n) external modes with n = 1,2,3, and m = n + 1 at values of beta similar or equal to 1%-2%. These modes are unstable in the circular tokamak at the same value of beta. If delta is a measure of the plasma boundary deformation, then windows of stability [delta(min)delta(max)] may exist depending strongly on equilibrium parameters. The results are described in terms of stability zones in the (q(axis),q(edge)) plane. (C) 1997 American Institute of Physics.