The optimization of a single bit string by means of iterated mutation and selection of the best (a (1+1)-Genetic Algotihm) is discussed with respect to three simple fitness functions: The counting ones problem, a standard binary encoded integer, and a Gray coded integer optimization problem. A mutation rate schedule that is optimal with respect to the success probability of mutation is presented for each of the objective functions, and it turns out that the standard binary code can hamper the search process even in case of unimodal objective functions. While normally a mutation rate of 1/l (where l denotes the bit string length) is recommendable, our results indicate that a variation of the mutation rate is useful in cases where the fitness function is a multimodal pseudo-boolean function, where multimodality may be caused by the objective function as well as the encoding mechanism.