A quasi-isodynamic stellarator with poloidally closed contours of the magnetic field strength B (Mikhailov 2002 Nucl. Fusion42 L23) has been obtained by an integrated physics optimization comprising MHD and neoclassical theory. For a configuration with six periods and aspect ratio approximately 12, a main result is the attainability of an essentially MHD-stable high-β (⟨ β⟩ ≈ 0.085) plasma with low neoclassical transport, approximately vanishing bootstrap current in the long-mean-free-path regime and excellent α-particle confinement.