Methyl α(and β)-D-3,4-anhydro-tagatofuranosides are important synthetic building blocks as they undergo regioselective ring-opening to afford exclusively products with the D-fructo configuration. Previous attempts to prepare these compounds from the corresponding methyl D-fructofuranosides under standard Mitsunobu conditions have led to an undesired 9:1 mixture of tagato and psico oxiranes. We now report that in the presence of added phenol, the tagato product is formed exclusively and in quantitative yield under extremely mild conditions. Similarly, both D- and L-methyl arabinofuranosides, gave the corresponding methyl 2,3-anhydro-D-lyxofuranosides and methyl 2,3-anhydro-L-lyxofuranosides in quantitative yields using this modified Mitsunobu protocol. The mechanism of this reaction appears to involve the intermediate formation of diphenoxytriphenylphosphorane, which acts as a selective Mitsunobu reagent for oxirane formation from fructo and arabino furanosides as well as trans-diaxial pyranoside diols such as those in levoglucosan. An unusual Mitsunobu-induced anomerisation reaction is also reported.