  Concentrating on the impact of the very recent top quark discovery, we
perform a combined analysis of two strongest constraints on the 2 Higgs doublet
model, one coming from the recent measurement by CLEO on the inclusive
branching ratio of b->s \gamma decay and the other from the recent LEP data on
Z->b b-bar decay. We have included the model predictions for one-loop vertex
corrections to Z->b b-bar through $\epsilon_b$. We find that the $\epsilon_b$
constraint excludes most of the less appealing window $\tan\beta\lsim 1$ at 95%
C.L. for the measured top mass from CDF, mt=176+/- 8+/-10 GeV. Moreover, it
excludes $\tan\beta\lsim 2$ at 95% C.L. for mt>176 GeV. Combining with the b->s
\gamma constraint, only very heavy charged Higgs (>670 GeV) is allowed by the
measured mt from CDF.
