The helically-deformed profiles of driven, dissipative magnetohydrodynamic equilibria (MONTGOMERY et al., 1989, Phys. Rev. A 40, 1515) are constructed through second order in helical amplitude. The resultant plasma configurations are presented in terms of contour plots of magnetic flux function, pressure, current flux function and the mass flux function, along with the stability boundary at which they are expected to appear. For the Wisconsin Phaedrus-T Tokamak, plasma profiles with significant m=3, n=1 perturbation seem feasible; for these, the plasma pressure peaks off-axis. For the smaller aspect ratio case, the configuration with m=1, n=1 is thought to be relevant to the density perturbation observed in JET after a pellet injection.