Monohydrated uracil (UW) complexes are stabilized by both O⋯HO and NH⋯O hydrogen bonds (H-bonds), simultaneously participating in forming three stable cyclic structures. The role and contribution of these individual H-bonds (O⋯HO and NH⋯O) to the stability of the three UW complexes are still not understood, because of the technical problems in obtaining their optimized structures by standard geometry optimization. The present study explores a non-standard approach to identify three single H-bonded local minima structures without imaginary frequency using DFT (M06-2X, B3LYP and B3LYP-D3), MP2 and CCSD(T) theories and Dunning's correlation-consistent aug-cc-pVTZ basis set, in both vacuum and aqueous media (CPCM method). The results reveal that these new structures are very shallow secondary minima between two deep wells or next to a deep well of primary minima (double H-bonded structures) in the potential energy surface. The H-bond energy of these single H-bonded complexes is found to be less sensitive to a wide range (about 15-20 degrees) of O⋯HO and NH⋯O angles, and the linearity is preferred in the stable three single H-bonded structures. The technical method used to locate such a shallow minimum is described in detail and may be useful for identifying local minima in other cases where consecutive multiple H-bonded structures are global minima. Energy decomposition (using symmetry adapted perturbation theory (SAPT)) of interaction energy, electron redistribution, and relevant vibrational modes are discussed.