This note considers the problem of finding a stable reduced-order model for a given stable model so that its H-2 model reduction cost differs by less than a prescribed error from the optimal cost, which may or may not be achievable. It is shown that this new version of the longstanding H-2 optimal model reduction problem can be reduced to a well-posed smooth constrained minimization problem whose global solution is guaranteed to exist. In addition, a globally convergent algorithm in the form of an ordinary differential equation is derived.