This study proposes to apply a structural reanalysis technique to an enumeration method for global optimization of discrete truss structures. The optimization problem is to find the sectional areas which minimize the truss structural volume from a list of standard sections under the stress and deflection constraints. At first, to reduce the computational effort, a structural reanalysis equation is derived, in which large number of unknown degrees of freedom are reduced. Next, a numerical generation method of relaxed linear constraints is also presented to reduce the number of structural analyses and re-analyses. The procedure of the enhanced enumeration method with above-mentioned two techniques is presented. The proposed method is applied to three trusses and compared with the structural analyses of all combinations.