Abstract A direct approach is presented to compare constant modulus (CM) and Wiener criteria, in the context of equalization with complex signals. It is based on an approximation of the cost function of the CM criterion by a function related to the Wiener cost function and symmetrical in terms of the equalizer coefficient vector H and − H. Two CM criteria are considered, namely CM (2,2) and CM (1,2). The analytical study of the CM (1,2) criterion leads to crucial results concerning its performance. It is shown that the equalizer coefficient vector is shrunken by the CM (2,2) criterion while it is stretched by the CM (1,2) criterion, with respect to the Wiener solution. In addition, for small values of the minimum mean square error, the CM (1,2) criterion outperforms the classical CM (2,2) criterion. The relative merits of the two CM criteria are clarified and CM (1,2) appears as a criterion of choice for blind equalization with complex signals.