The controlled synthesis of PbSe nanocrystal quantum dots with narrow size distributions was achieved through phase decomposition of the PbSe solid solution in a phosphate glass host. Structural characterization by electron microscopy and x-ray diffraction shows that the dots have mean diameters between 2 and 15 nm. The exciton Bohr radiusaB=46 nmin PbSe, so these quantum dots provide unusual and perhaps unique access to the regime of strong quantum confinement. The optical absorption spectra are compared to the predictions of a theoretical treatment of the electronic structure. The theory agrees well with experiment for dots larger than∼7 nm,but for smaller dots there is some deviation from the theoretical predictions. ©1997 American Institute of Physics.