A systematic examination of the components of the interaction energy, obtained with the Kitaura and Morokuma method, for nine H-bonded dimers without and with counterpoise corrections (CP) is presented.The nine dimers H,A . . . HBH, correspond to all the possible combinations of HF, H,O, and NH, as electron donors and electron acceptors. The interaction energy and the corresponding components have been computed over a sizable interval of intermolecular distances with five basis sets (sTO-~G, MINI-I, 3-21G. 4-31G, 6-31G**) selected among those most extensively used to study interactions in larger systems. The CP corrections to the AE components have been obtained with a method, implemented in our group, which permits assignment to the pertinent components of AE of a physically reasonable portion of the CP correction even though different CP corrections are adopted. We examine here three versions of the CP correction, namely, the full CP correction (i.e., the original version of Boys and Bernardi) and CP corrections limited to the virtual space of the partner or to the electron donor only. The resulting data are employed to assess the basis set dependence of several models of hydrogen bonding (the electrostatic model, the semiclassical model, etc.) both with and without CP corrections.