  We measure the inclusive branching fractions of charm mesons into three
mesons with large s-anti-s content, namely the eta, eta' and phi. Data were
accumulated with the CLEO-c detector. For D0 and D+ rates, we use 281/pb taken
on the psi(3770) resonance, and for Ds+ rates, we use 195/pb taken at 4170 MeV.
We find that the production rates of these particles are larger in Ds+ decays
than in D0 and D+ decays. The phi rate, in particular, is 15 times greater.
These branching fractions can be used to measure Bs yields either at the
Upsilon(5S) resonance or at hadron colliders.
