The possibility of fulfilling the condition of poloidal closure of the contours of the second adiabatic invariant for all reflected particles is studied for systems with poloidally closed contours of the magnetic field B on the magnetic surfaces through computational stellarator optimization. It is shown that by adjusting the geometry this is possible in a major fraction of the plasma volume. The most salient characteristic (as compared to previous quasi-isodynamic configurations) is a magnetic axis whose curvature vanishes in all cross sections with an extremum of B on the magnetic axis and renders possible a three-dimensional structure of B with unprecedentedly high collisionless alpha-particle confinement.