The paper presents the asymptotical analysis of a technique for improving the convergence of evolution strategies (ES) on noisy fitness data. This technique that may be called “Mutate large, but inherit small”, is discussed in light of the EPP (evolutionary progress principle). The derivation of the progress rate formula is sketched, its predictions are compared with experiments, and its limitations are shown. The dynamical behavior of the ES is investigated. It will be shown that standard self-adaptation has considerable problems to drive the ES in its optimum working regime. Remedies are provided to improve the self-adaptation.