The plasma convective (flute-interchange) stability for low magnetic shear systems, with a low collisionality and a low beta, is considered in terms of the necessary and sufficient collisionless kinetic criterion. The magnetic confinement systems under consideration are axially symmetric mirrors equipped with outer divertors and inner field reversing rings (cusps, internal rings, high-beta cells) and closed multimirror traps. A simple approach is proposed for plasma stabilization resulting in a substantial steepening of the critical pressure profile. The essence is the combination of the plasma stabilization by a strong and an alternating-sign field-line curvature. Axially symmetric tandem mirror systems composed of a mirror device having an outer divertor and an inner field reversing ring are shown to have an internal radially peaked stable pressure profile. Bumpy tori are also shown to have an internally peaked stable pressure profile.