We study the structure of electronic states in individual PbS nanocrystal quantum dots by scanning tunneling spectroscopy (STS) using one-to-two monolayer nanocrystal films treated with 1, 2-ethanedithiols (EDT). Up to six individual valence and conduction band states are resolved for a range of quantum dot sizes. The measured states' energies are in good agreement with calculations using the k · p four-band envelope function formalism. A comparison of STS and optical absorption spectra indicates that some of the absorption features can only be explained by asymmetric transitions involving the states of different symmetries (e.g., S and P or P and D), which points towards the relaxation of the parity selection rules in these nanostructures. STS measurements also reveal a midgap feature, which is likely similar to one observed in previous charge transport studies of EDT-treated quantum dot films.