An alternative approach to formulating a special class of linear goal programming (LGP) models is presented. We propose a formulation of the LGP model that can include the decision variables in the objective function. We specifically propose that the position of the decision variables in the objective function be used to eliminate goal constraints whose sole purpose is to indirectly optimize decision variables. For the select group of LGP problems wherever indirect optimization of decision variables are sought, the alternative LGP model formulation is able to reduce the size of these LGP models and in turn the computational effort required for their solution.