  We analyze how the CFL states in dense matter work in the direction of
enhancing the parameter space for absolutely stable phases (strange matter). We
find that the "CFL strange matter" phase can be the true ground state of
hadronic matter for a much wider range of the parameters of the model (the gap
of the QCD Cooper pairs $\Delta$, the strange quark mass $m_s$ and the Bag
Constant $B$) than the state without any pairing, and derive a full equation of
state and an accurate analytic approximation to the lowest order in $\Delta$
and $m_{s}$ which may be directly used for applications. The effects of pairing
on the equation of state are found to be small (as previously expected) but not
negligible and may be relevant for astrophysics.
