  Kamlah's second order method for approximate particle number projection is
applied for the first time to variational calculations with effective forces.
High spin states of normal and superdeformed nuclei have been calculated with
the finite range density dependent Gogny force for several nuclei. Advantages
and drawbacks of the Kamlah second order method as compared to the
Lipkin-Nogami recipe are thoroughly discussed. We find that the Lipkin-Nogami
prescription occasionally may fail to find the right energy minimum in the
strong pairing regime and that Kamlah's second order approach, though providing
better results than the LN one, may break down in some limiting situations.
