The interplay between groups of water molecules and single-atom contacts, as reflected in the electrical conductances and mechanical forces of copper atomic junctions, is explored by means of first-principles theory and semi-empirical calculations. We study the influence of the atomic geometries of copper electrodes with pyramidal and non-crystalline structures in the presence and absence of water on the conductance profiles as the electrodes approach each other. It is shown that the atomic arrangements of nano-contacts have crucial effects on the formation of plateaus and the conductance values. Groups of hydrogen bonded water molecules bridge the junction electrodes before a direct Cu-Cu contact between the electrodes is made. However, the bridging of the two copper electrodes by a single H2O molecule only occurs in the junctions with pyramidal electrodes. Our findings reveal that the presence of H2O molecules modifies strongly the conductance profile of these junctions. In the absence of water molecules, the pyramidal junctions exhibit continuous transitions between integer conductance plateaus, while in the presence of H2O molecules, these junctions show abrupt jump to contact behavior and no well-defined conductance plateaus. By contrast, in the absence of H2O molecules, the non-crystalline junctions display jump to contact behavior and no well-defined plateaus, while in the presence of H2O molecules they exhibit a jump to contact and abrupt transitions between fractional and integer plateaus.