The size dependence of the electronic spectrum of InAs nanocrystals ranging in radius from 10-35 Angstrom has been studied by size-selective spectroscopy. An eight-band effective mass theory of the quantum size levels has been developed which describes the observed absorption level structure and transition intensities very well down to smallest crystal size using bulk band parameters. This model generalizes the six-band model which works well in CdSe nanocrystals and should adequately describe most direct semiconductor nanocrystals with band edge at the Gamma-point of the Brillouin zone.