We present alpha-expansion beta-shrink moves, a simple generalization of the widely-used alpha-beta swap and alpha-expansion algorithms for approximate energy minimization. We show that in a certain sense, these moves dominate both alpha-beta-swap and alpha-expansion moves, but unlike previous generalizations the new moves require no additional assumptions and are still solvable in polynomial-time. We show promising experimental results with the new moves, which we believe could be used in any context where alpha-expansions are currently employed.