  The high energy events observed at the IceCube Neutrino Observatory have
triggered many investigations interpreting the highly energetic neutrinos
detected as decay products of heavy unstable Dark Matter particles. However,
while very detailed treatments of the IceCube phenomenology exist, only a few
references focus on the (non-trivial) Dark Matter production part -- and all of
those rely on relatively complicated new models which are not always testable
directly. We instead investigate two of the most minimal scenarios possible,
where the operator responsible for the IceCube events is directly involved in
Dark Matter production. We show that the simplest (four-dimensional) operator
is not powerful enough to accommodate all constraints. A more non-minimal
setting (at mass dimension six), however, can do both fitting all the data and
also allowing for a comparatively small parameter space only, parts of which
can be in reach of future observations. We conclude that minimalistic
approaches can be enough to explain all data required, while complicated new
physics seems not to be required by IceCube.
