  A simple and efficient method to treat nuclear pairing correlations within a
simple Hartree-Fock--plus-BCS description is proposed and discussed. It relies
on the fact that the intensity of pairing correlations depends crucially on
level densities around the Fermi surface ($ \rho(e_F)$) and that any fitting of
nuclear energies as functions of the nucleon numbers is akin of a
semi-classical average, smoothing out their quantal structure. A particular
attention has been paid to two points generally ignored in previous similar
approaches. One is a correction advocated by M\"{o}ller and Nix [Nucl. Phys. A
536, 20 (1992)] taking into account the fact that the data included into the
fit correspond to $ \rho(e_F)$ values systematically lower than average. The
second is due to a systematic overestimation of the proton sp level density at
the Fermi surface resulting from the local Slater approximation of the Coulomb
terms in use in most microscopic descriptions. Our approach is validated by the
agreement with data of corresponding calculated moments of inertia of well and
rigidly deformed rare-earth nuclei, evaluated according to the Inglis-Belyaev
ansatz with some crude Thouless-Valatin corrections. Indeed, the agreement
which is found, is at least of the same quality as what results from a specific
fit of the pairing intensities to these particular pieces of data. While this
approach is currently limited to the very simple seniority force pairing
treatment, it may serve as a starting point to define pairing residual
interactions from averaged odd-even mass differences data, using merely average
sp level densities associated to calculated canonical basis.
