This paper is devoted to the analysis of small central composite designs obtained with a regular fraction of resolution III *. We show that it is then possible to find explicitely mean square estimators, predicted response, variance dispersion graphs and D-efficiency. Such designs, well chosen, can be an alternative to classical CCD when the priority is to reduce the number of runs. Keywords Central composite designs; regular fractions of resolution III * or V; variance dispersion graphs; D-efficiency.