Low aspect ratio tokamaks (LATs) can potentially provide a high ratio of plasma pressure to magnetic pressure beta and high plasma current I at a modest size. This opens up the possibility of a high-power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma current, which requires operating at high beta(p). A high value of the Troyon factor beta(N) and strong shaping is required to allow simultaneous operation at a high-P and high bootstrap fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect ratio 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both beta(N) and beta are defined in terms of the vacuum toroidal field. Equilibria with beta(N) greater than or equal to 8 and beta similar to 35%-55% exist that are stable to n=infinity ballooning modes. The highest beta case is shown to be stable to n=0,1,2,3 kink modes with a conducting wall. (C) 1997 American Institute of Physics.