This work summarises the present understanding of the expected MSSM SUSY
Higgs reach for CMS. Many of the studies presented here result from detailed
detector simulations incorporating final CMS detector design and response. With
30 fb-1 the h -> gamma,gamma and h -> bb channels allow to cover most of the
MSSM parameter space. For the massive A,H,H+ MSSM Higgs states the channels A,H
-> tau,tau and H+ -> tau,nu turn out to be the most profitable ones in terms of
mass reach and parameter space coverage. Consequently CMS has made a big effort
to trigger efficiently on taus. Provided neutralinos and sleptons are not too
heavy, there is an interesting complementarity in the reaches for A,H ->
tau,tau and A,H -> chi,chi.Comment: 19 pages, 27 figure