Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma–vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number n = 1 distortions when the edge bootstrap current is large and higher n corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch–Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch–Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.