During a primary immune response generally two classes of antibody are produced, immunoglobulin M (IgM) and immunoglobulin G (IgG). It is currently thought that some lymphocytes which initially produce IgM switch to the production of IgG with the same specificity for antigen. During a secondary immune response IgG is the predominant antibody made throughout the response. In this paper we address the question of why such apparently complicated modes of response should have been adapted by evolution. We construct mathematical models of the immune response to growing antigens which incorporate complement dependent cell lysis. By comparing the times required to eliminate antigen we show that under certain conditions it is advantageous for an animal to switch some of its lymphocytes from IgM to IgG production during a primary response, but yet to secrete only IgG during a secondary response. The sensitivity of such a conclusion to parameter variations is studied and the biological basis and implications of our models are fully discussed.