Evolutionary programs are capable of finding good solutions to difficult optimization problems. Previous analysis of their convergence properties has normally assumed the strategy parameters are kept constant, although in practice these parameters are dynamically altered. In this paper, we propose a modified version of the 1/5-success rule for self-adaptation in evolution strategies (ES). Formal proofs of the long-term behavior produced by our self-adaptation method are included. Both elitist and non-elitist ES variants are analyzed. Preliminary tests indicate an ES with our modified self-adaptation method compares favorably to both a non-adapted ES and a 1/5-success rule adapted ES.