High-level ab initio calculations (B3LYp/6-31+G** and QCISD(T)/6-311+G**) were carried out to resolve the disagreement between recent experimental and computational estimates of the relative strength of the intramolecular hydrogen bond in Z-hydrogen maleate anion with respect to the normal hydrogen bond in maleic acid. The computational estimates for the strength of the intramolecular hydrogen bond in the gasphase maleate anion are in a range of 14-28 kcal/mol depending on the choice of the reference structure. Computational data suggest that the electrostatic influence of a counterion such as a tetraalkylammonium cation can considerably weaken the hydrogen bonding interaction (by 1.5-2 times) in the complexed hydrogen maleate anion relative to that in the naked anion. The estimated internal H-bonding energies for a series of Z-maleate/R4N+ salts (R = CH3, C2H5, CH3CH2CH2CH2) range from 8 to 13 kcal/mol, The calculated energy differences between the E- and Z-hydrogen maleates complexed to Me4N+, Et4N+, and Bu4N+ cation are 4.9 (B3LYP/6-31+G(d,p)) and 5.7 and 5.8 kcal/mol (B3LYP/6-31G(d)). It is also demonstrated that the sodium cation exerts a similar electrostatic influence on the hydrogen bond strength in bifluoride anion (FHF-). The present study shows that while low-barrier short hydrogen bonds can exist in the gas phase (the ban er for the hydrogen transfer in maleate anion is only 0.2 kcal/mol at the QCISD(T)/6-311+G**//QCISD/6-31+G** level), whether they can also be strong in condensed media or not depends on how their interactions with their immediate environment affect their strength.