XRD, UV-Vis, EXAFS, XANES, and Raman techniques have been used to study the removal of water molecules coordinated to the Cu(II) framework atoms of the novel HKUST-1 metal-organic framework. The dehydration process preserves the crystalline nature of the material, just causing a reduction of the cell volume due to the shrinking of the [Cu2C4O8] cage. The removal of adsorbed H2O molecule makes the framework Cu(II) sites available for interaction with other probe molecules. In situ IR spectroscopy has evidenced the formation at liquid nitrogen temperature of labile Cu(II)⋯CO adducts characterized by a ṽ(C-O) = 2178 cm-1 and at 15 K of Cu(II)⋯H2 adducts characterized by a ṽ(H-H) = 4100 cm-1. To the best of our knowledge, we have observed for the first time a clear signal of Cu(II) carbonyl and dihydrogen complexes formed inside a crystalline microporous hosting matrix. The sinking of the oxygens of the carboxyl units, undergone by the Cu(II) framework ions in the dehydration process, is responsible for the rather low coordinative unsaturation of Cu(II). The important shielding effect of the four oxygen framework atoms is testified by the low polarization factor of the Cu(II) site probed by both CO and H2 molecules.