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The trends with mass number are examined for the odd-even-staggering (OES) innuclear binding of neutrons and protons through the conventional measures  $\Delta^{(3)}$. The large differences previously observed between thesetrends for even and odd values of these measures is found to arise, in part,from the slow variation of binding energies with mass and charge which providesa background contribution. This background is estimated with the liquid-dropmodel, and accounts for the greater difference found in proton removal relativeto neutron removal. The differences which persist after backgrounds are removedcan not be treated in the conventional liquid-drop model but require theaddition of a new term. Such a term is investigated, and its effect on specificvalues of the OES is calcutated. The liquid-drop fitting is also applied to aset of separation energies constrained to match the specific set of nuclei usedto determine the observed values for the odd $\Delta^{(3)}$. The resulting fitfor the pairing term is compared to the average value of even and odd measures.The effect on this value of the new liquid-drop term is observed, and thechange in background when the new term is included is also used as an alternatemethod for determining the difference between trends of the even and odd valuesof the OES.

Odd-even staggering in nuclear binding and the liquid-drop model