  We describe the Fortran code CPsuperH2.3, which incorporates the following
updates compared with its predecessor CPsuperH2.0. It implements improved
calculations of the Higgs-boson masses and mixing including stau contributions
and finite threshold effects on the tau-lepton Yukawa coupling. It incorporates
the LEP limits on the processes e^+ e^- to H_i Z, H_i H_j and the CMS limits on
H_i to tau^+ tau^- obtained from 4.6/fb of data at a centre-of-mass energy of 7
TeV. It also includes the decay mode H_i to Z gamma and the Schiff-moment
contributions to the electric dipole moments of Mercury and Radium225, with
several calculational options for the case of Mercury. These additions make
CPsuperH2.3 a suitable tool for analyzing possible CP-violating effects in the
MSSM in the era of the LHC and a new generation of EDM experiments
