The extent to which the methods of superconductivity theory are reliable when applied to the calculation of the properties of deformed nuclei is examined numerically. The exact eigenstates for an even or odd number of particles moving in nine or fewer evenly spaced levels, and interacting via a pairing force (whose magnitude is dictated by the observed odd-even mass differences) provide the basis for comparison. The following are examined: (1) the BCS-Bogoliubov approximations to the ground and excited states, (2) the modifications to account for “blocking” of levels by unpaired particles, (3) projection of that part of the wave function containing the correct number of particles, and (4) the dependence on the self-energy term (−Gν2). To block before solving the BCS equations does not appear to be warranted. Indeed for beta-decay hinderance factors, the least sophisticated method (1) is as adequate as the rest coming to within 5–10% of the exact values. The calculation of spectra is considerably improved by projecting, but again only the ground state parameters need be used. None of the methods consistently approximates the occupation factors of the (uανβ + σναuβ)2 and (uαuβ + σνανβ)2 type to better than 20% for σ = −1, and 10% for σ = +1. However, either blocking-without-projecting or projecting with the unblocked parameters are often equally satisfactory. The degree to which the small number of levels considered here has a bearing on these results is examined.