  The origin of an anomalous excess of high-energy (about 100 GeV and higher)
positrons in cosmic rays is one of the rare problems in this field, which is
proposed to be solved with dark matter (DM). Attempts to solve this problem are
faced with the issue of having to satisfy the data on cosmic positrons and
cosmic gamma radiation, which inevitably accompanies positron production, such
as FSR (final state radiation), simultaneously. We have been trying to come up
with a solution by means of two approaches: making assumptions (*) about the
spatial distribution of the dark matter and (**) about the physics of its
interactions. This work is some small final step of a big investigation
regarding the search for gamma suppression by employing the second approach,
and a model with a doubly charged particle decaying into two positrons (X++
$\rightarrow$ e+ e+) is suggested as the most prospective one from those
considered before.
