  It is well known that the annihilation of Majorana dark matter into fermions
is helicity suppressed. Here, we point out that the underlying mechanism is a
subtle combination of two distinct effects, and we present a comprehensive
analysis of how the suppression can be partially or fully lifted by the
internal bremsstrahlung of an additional boson in the final state. As a
concrete illustration, we compute analytically the full amplitudes and
annihilation rates of supersymmetric neutralinos to final states that contain
any combination of two standard model fermions, plus one electroweak gauge
boson or one of the five physical Higgs bosons that appear in the minimal
supersymmetric standard model. We classify the various ways in which these
three-body rates can be large compared to the two-body rates, identifying cases
that have not been pointed out before. In our analysis, we put special emphasis
on how to avoid the double counting of identical kinematic situations that
appear for two-body and three-body final states, in particular on how to
correctly treat differential rates and the spectrum of the resulting stable
particles that is relevant for indirect dark matter searches. We find that both
the total annihilation rates and the yields can be significantly enhanced when
taking into account the corrections computed here, in particular for models
with somewhat small annihilation rates at tree-level which otherwise would not
be testable with indirect dark matter searches. Even more importantly, however,
we find that the resulting annihilation spectra of positrons, neutrinos,
gamma-rays and antiprotons differ in general substantially from the
model-independent spectra that are commonly adopted, for these final states,
when constraining particle dark matter with indirect detection experiments.
