In this paper we describe a new class of representations for real-valued parameters called Center of Mass Encoding (CoME). CoME is based on variable length strings, it is self-adaptive, and it permits the choice of the degree of redundancy of the genotype-to-phenotype map and the choice of the distribution of the redundancy over the space of phenotypes. We first describe CoME and then proceed to test its performance and compare it with other representations and with a state-of-the-art evolution strategy. We show that CoME performs well on a large set of test functions. Furthermore, we show how CoME adapts the granularity of its discretization on functions defined over nonuniformly scaled domains.