  In a degenerate scheme with mass m_0 a complete analysis of the allowed range
of the effective electron neutrino Majorana mass <m> is performed. Special
attention is paid to effects of cancellations caused either by intrinsic CP
parities of the eigenstates (CP invariance) or by complex mixing matrix
elements (CP violation). We investigate all possibilities and give in each case
constraints on the phases, the relative CP parities or the neutrino mass scale.
A solar mixing angle \sin^2 2 \theta smaller than 0.7 jeopardizes the
degenerate mass scheme. A key value of <m>/m_0 is identified, which is
independent on the solar solution and would rule out certain schemes. Also it
would answer the question regarding the presence of CP violation. Even if a
total neutrino mass scale and an effective mass is measured, the value of the
phases or parities is not fixed, unless in some special cases. The resulting
uncertainty in the other mass matrix elements is at least of the same order
than the one stemming from nuclear matrix elements calculations.
