Three 1,6-anhydro-2-deoxy-β-D-hexopyranoses with the arabino-(XIV), lyxo-(XVIII), and ribo-(XIX) configurations have been synthesized. Hydrolysis of each of these compounds was rapid and proceeded essentially to completion. Their optical rotations are consistent with a chair-like conformation. 1,6:2,3- and 1,6:3,4-Dianhydro-β-D-allopyranoses, (XI) and (XIII), have also been prepared; these complete the series of isomeric epoxide derivatives of the 1,6-anhydro-D-hexopyranoses.