The present paper revisits the problem of minimizing the weight of 2D skeletal structures under a single displacement constraint. The contribution lies on the development of an optimization procedure implementing three new features. The first feature is the formulation of a new and efficient Optimality Criterion-type redesign scheme where no Lagrange multipliers are required. The second feature is the introduction of a new categorization of the structural elements according to which members simultaneously being force-passive and area-active may lead search methods to local minima. The third feature is the application of a typical line-search optimization method on the structural elements diagnosed as force-passive/area-active so that their contribution to the structural weight is minimized and a better design is obtained. The validity of the proposed optimization procedure was successfully tested for determinate and indeterminate skeletal structures.