  By exploiting the full process $p\bar p\to t\bar b H^-$, in place of the
standard Monte Carlo procedure of factorising production and decay, $p\bar p\to
t\bar t$ followed by $\bar t\to\bar b H^-$, we show how to improve the
discovery reach of the Tevatron (Run 2) in charged Higgs boson searches, in the
large $\tan\beta$ region. This is achieved in conjunction with dedicated cuts
on a `transverse mass' distribution sensitive to the Higgs boson mass and to
`polarisation' effects in the $H^-\to\tau^-\bar\nu_\tau$ decay channel.
