  A complete intersection of n polynomials in n indeterminates has only a
finite number of zeros. In this paper we address the following question: how do
the zeros change when the coefficients of the polynomials are perturbed? In the
first part we show how to construct semi-algebraic sets in the parameter space
over which all the complete intersection ideals share the same number of
isolated real zeros. In the second part we show how to modify the complete
intersection and get a new one which generates the same ideal but whose real
zeros are more stable with respect to perturbations of the coefficients.
