In this chapter, we review the optimality results for the estimation of parameters and subset of parameters of the Scheffé’s mixture models while the factor space is the entire simplex, i.e., while we are in the framework of an unconstrained factor space. Though most of the results are related to quadratic model, optimality results for linear- and higher-degree polynomials are also discussed. Kiefer’s equivalence theorem plays an important role in characterizing optimum designs. It has been observed that the support points of an optimum design under different optimality criteria belong to the subclass of union of barycenters. © 2014, Springer India.