  Complete one-loop results for the decay widths of neutral Higgs bosons (h_a)
into lighter neutral Higgs bosons (h_b, h_c) are presented for the MSSM with
complex parameters. The results are obtained in the Feynman-diagrammatic
approach, taking into account the full dependence on the spectrum of
supersymmetric particles and all complex phases of the supersymmetric
parameters. The genuine triple-Higgs vertex contributions are supplemented with
two-loop propagator-type corrections, yielding the currently most precise
prediction for this class of processes. The genuine vertex corrections turn out
to be very important, yielding a large increase of the decay width compared to
a prediction based on the tree-level vertex. The new results are used to
analyse the impact of the experimental limits from the LEP Higgs searches on
the parameter space with a very light MSSM Higgs boson. It is found that a
significant part of the parameter space of the CPX benchmark scenario exists
where channels involving the decay h_2 --> h_1 h_1 have the highest search
sensitivity, and the existence of an unexcluded region with M_{h_1} \approx 45
GeV is confirmed.
