The diameter dependence of the optical band gap of single CdSe nanowires (NWs) is investigated by a combination of atomic force microscopy, scanning fluorescence microscopy, and transmission electron microscopy. We find a good congruence of the experimental data to calculations within the effective mass approximation taking into account quantization, exciton Coulomb interaction, and dielectric mismatch. The experimental data are furthermore compared to different theoretical approaches. We discuss the influence of alternating wurtzite and zinc blende segments along the NWs on their optical properties.