The primary objective of spring design is to obtain a spring which will do the required job and at the same time be the most economical for a given application. This means that the spring must fit into the available space and has a satisfactory life in service. The optimum springs would then have minimum weight, minimum length or minimum space. Various optimum values of wire diameter and spring index are obtained. These are evaluated in a closed form or utilizing iterative search techniques. The problem is formulated with and without the variation of the maximum shear stress with the wire diameter. The optimal parameters are also normalized and plotted.