InAs/GaAs quantum dots (QDs) grown on a GaAs (001) substrate were studied by photoluminescence spectroscopy. Both C2v and D3h QDs with featured XX11, X11+, and XX21+ spectra have been found. A local defect field tunes the dominant exciton from X+ to X or X−, enhances the population on XX, XXX, and XXX−, and induces tunneling and spectral diffusion. In D3h QDs, it also induces a prior e1–h2 transition and a structural polarization of XX21+ and XX11 to build a direct cascade XX21+ − X+. Both XX21+ − X+ and XX − X have no fine structure splitting, promising for entangled photon pair emission. A dominant X+ with slow electron capture (due to background holes) proves a pure single-photon emission.