The pairing contribution to the odd-even oscillations in the nuclear binding energies is considered in the framework on the nuclear shell model.  Schematic and realistic Hamiltonians are used to understand the trends related to pairing and shell gaps. Detailed results are shown and discussed for the calcium isotopes. The pairing gap for 53Ca obtained from new experimental data on the masses of 52-54Ca shows the smallest value yet observed. This is explained as being due to shell gaps around the low-j orbital 1p1/2. Minima in the pairing gaps for all nuclei are shown and discussed.