  We present an improved partial wave analysis of the dominant LSP annihilation
channel to a fermion-antifermion pair which avoids the non-relativistic
expansion being therefore applicable near thresholds and poles. The method we
develop allows of contributions of any partial wave in the total angular
momentum J in contrast to partial wave analyses in terms of the orbital angular
momentum L of the initial state, which is usually truncated to p-waves, and
yields very accurate results. The method is formulated in such a way as to
allow easy handling of CP-violating phases residing in supersymmetric
parameters. We apply this refined partial wave technique in order to calculate
the neutralino relic density in the constrained MSSM (CMSSM) in the presence of
CP-violating terms occurring in the Higgs - mixing parameter \mu and trilinear
A coupling for large tanb. The inclusion of CP-violating phases in mu and A
does not upset significantly the picture and the annihilation of the LSP's to a
b b_bar, through Higgs exchange, is still the dominant mechanism in obtaining
cosmologically acceptable neutralino relic densities in regions far from the
stau-coannihilation and the `focus point'. Significant changes can occur if we
allow for phases in the gaugino masses and in particular the gluino mass.
