Interaction between shear flows and plasma instabilities in axially symmetric mirrors can lead to improved confinement, observed both in experiments on the gas dynamic trap and in simulations. Shear flows, driven via biased end plates and limiters, in combination with finite-larmor-radius effects are shown to be efficient in confining high-beta plasmas even with a magnetic hill on axis. Interpretation of observed effects such as vortex confinement, i.e., confinement of the plasma core in the dead-flow zone of the driven vortex, is shown to agree well with simulations. Theoretical scaling laws predict such a confinement scheme to be useful even in fusion plasmas.