The conditions are obtained for confining a plasma of arbitrary asymmetry, plasma beta, and collisionality, in an equilibrium configuration free of neoclassical transport. Such omnigeneous scalar pressure equilibria are shown to exist if, and only if, the divergence of the parallel current density vanishes, while for an anisotropic pressure other mild restrictions are needed. Explicit constraints are derived for axisymmetric tori and long‐thin, low‐beta conventional and tandem mirrors.