Ideal MHD limits to beta and bootstrap fraction are computed for pressure profiles similar to those of JET discharges with both internal and H mode transport barriers. Several non-monotonic current profiles are tested, and the pressure profile is constrained so that no negative current drive is required in steady state. Calculations are made both with and without an ideally conducting wall. The main result is that, for such peaked pressure profiles, the limits to beta and bootstrap fraction improve at low internal inductance, in particular when wall stabilization is taken into account. The highest limits to beta, and often also to normalized beta, occur for the maximum plasma current. There is also a weak dependence on qmin, for which three favourable regions have been identified. A highly advantageous region is found at qmin ≃ 1.6, where the limits to β* are 7.0% with, and 4.8% without, wall stabilization. The corresponding limits are 68 and 50%, respectively, for the bootstrap fraction and 4.0 and 2.9 for the normalized beta. These equilibria have low internal inductance, li = 0.62. For higher inductance, an optimum occurs when qmin ≃ 1.2, where the limit to β* is 5.3% with a wall and 4.7% without. The corresponding bootstrap fractions are about 46 and 38%, respectively. A third type of equilibrium that is interesting for steady state operation has qmin ≃ 2.1 and low inductance. Here the β* limits are lower, 4.9 and 3.4%, but the bootstrap fractions are higher, 77 and 60%.