We discuss efficient forward selection in the class of decomposable graphical models. This subclass of graphical models has a number of desirable properties. The contributions of This work are twofold. First we improve an existing algorithm by addressing cases previously not considered. Second we extend the algorithm to reflect model graphs with multiple disconnected components. We further present experimental results that apply this approach to a real dataset and discuss its properties. We belief that the presented approach is applicable to a wide area of fields and problems.