J.M. Greene (1987) created a class of analytic high- beta tokamak equilibria which had the virtue of being both simple and without artificial constraints on the possible values of beta . The equilibria were characterized by current profiles that are strongly peaked on the outside of the torus and by non-monotonic q-profiles which decrease towards the plasma boundary. The authors have constructed a straightforward extension of this class of analytic equilibria, which allows for more standard tokamak profiles, also at high beta . This extension is smoothly connected onto the original class of equilibria found by Greene through the well-known analytic high- beta Tokamak equilibrium constructed by F.A. Haas (1972), which serves as the transition point to the equilibria discussed here.