We report the synthesis and characterization of Pb-chalcogenide fused quantum-dot (QD) dimer structures. The resulting QD dimers range in length from 6 to 16 nm and are produced by oriented attachment of single QD monomers with diameters of 3.1-7.8 nm. QD monomers with diameters exceeding about 5 nm appear to have the greatest affinity for QD dimer formation and, therefore, gave the greatest yields of fused structures. We find a new absorption feature in the first exciton QD dimer spectra and assign this to a splitting of the 8-fold degenerate 1S-level. The dimer splitting increases from 50 to 140 meV with decrease of the QD-monomer size, and we present a mechanism that accounts for this splitting. We also demonstrate the possibility of fusing two QDs with different sizes into a heterostructure.