Zolotarev's Approximation problem consists in finding the best approximation of a polynomial of degree n by a polynomial of degree n−2 in the interval [−1, 1]. It is solved for n ≤ 12 by replacing CAD (Cylindrical Algebraic Decomposition) by a strategy consisting in computing first the Zariski closure of the semi-algebraic set which is looked for, before managing the inequalities.