We propose a mechanism by which changes of the mechanical tension of a composite lipid membrane are buffered by the invagination of membrane domains. We show that domain invagination, driven by differences in chemical composition, is a first-order transition controlled by membrane tension. The invaginated domains play the role of a membrane reservoir, exchanging area with the main membrane, and impose an equilibrium tension entirely controlled by their mechanical properties. The dynamical response of the reservoir reflects the tension-dependent kinetics of the domain shape transition, so that the tension of such a composite membrane is inherently transient and dynamical. The implications of this phenomenon for the mechanical properties of the membranes of living cells, where invaginated membrane domains are known to exist, are discussed.