In this paper we introduce modified versions of CMA-ES with the objective to help to prove convergence of CMA-ES. In order to ensure that the modifications do not alter the performances of the algorithm too much, we benchmark variants of the algorithm derived from them on problems of the bbob test suite. We observe that the main performances losses are observed on ill-conditioned problems, which is probably due to the absence of cumulation in the adaptation of the covariance matrix. However, the versions of CMA-ES presented in this paper have globally similar performances to the original CMA-ES.