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The aim of restricted D-and G-optimal designs introduced by Stigler is to deal with the linear regression model with the possible occurrence of a quadratic term. In this paper, the idea has been extended to A-, and Q-optir~~alities as well as to general polynomial regression models. Some interesting results have been found in the case of linear regression with the possiblc occurrence of quadratic and cubic terms. In some situations: the socalled Ck-restricted optimal designs for this regression model can 11e solved explicitly.