  We study the implications of phenomenological processes on a two-singlet
extension of the Standard Model we introduced in a previous work to describe
light cold dark matter. We look into the rare decays of $\Upsilon $ and $B$
mesons, most particularly the invisible channels, and study the decay channels
of the Higgs particle. Preferred regions of the parameter space are indicated,
together with others that are excluded. Comments in relation to recent Higgs
searches and finds at the LHC are made.
