Idiotypic interactions may be a factor in the selection of the B cell repertoire. Simulations of an evolving idiotypic network where new clones are introduced on a daily basis have shown that macroscopic properties, such as network size and connectivity, attain stationary values despite the rapid turnover of individual clones, indicating that idiotypic networks possess self-organizing properties. Affinities between antibodies were either zero, low (0.1), or high (1.0) in these simulations. It has been suggested that network properties may change when affinities take arbitrary real values. Here we show that the previous results of De Boer & Perelson on network size and connectivity are not changed when affinities take many different, closely spaced values.