A comparative theoretical study on the reactivity of the complexes [ReY(CO)3(bipy)] (Y = NH2, NHMe, NHpTol, OH, OMe, OPh, PH2, PHMe, PMe2, PHPh, PPh2, PMePh, SH, SMe, SPh; bipy = 2,2′-bipyridine) towards methyl propiolate was carried out to analyze the influence of both the heteroatom (N, O, P, S) and the alkyl and/or aryl substituents of the Y ligand on the nature of the product obtained. The methyl substituent tends to accelerate the reactions. However, an aromatic ring bonded to N and O makes the reaction more difficult, whereas its linkage to P and S favour it. On the whole, ligands with O and S heteroatoms seem to disfavour these processes more than ligands with N and P heteroatoms, respectively. Phosphido and thiolato ligands tend to yield a coupling product with the bipy ligand, which is not the general case for hydroxo, alcoxo or amido ligands. When the Y ligand has an O/N and an H atom the most likely product is the one containing a coupling with the carbonyl ligand, which is not always obtained when Y contains P/S. Only for OMe and OPh, the product resulting from formal insertion into the Re-Y bond is the preferred.