Using atomistic empirical pseudopotentials, we havecalculated the electronic structures of CdSe nanowires with a bulgedarea. The localized state wavefunctions and their binding energies arecalculated, and their dependences on the bulged area shape are analyzed.We find that both the binding energy and the wavefunction localizationstrongly depend on the bulged area shape, with the most compact shapeproduces the largest binding energy and strongest wavefunctionlocalization. We also find that the top of the valence band state has aweaker localization than the bottom of the conduction band state due toan effective mass anisotropy