  Barrientos Bendezu' and Kniehl [hep-ph/9807480] recently suggested that
$W^\pm H^\mp$ associated production may be a useful channel in the search for
the elusive heavy charged Higgs bosons of the 2 Higgs Doublet Model at the
Large Hadron Collider. We investigate the phenomenology of this mechanism in
the Minimal Supersymmetric Standard Model, with special attention paid to the
most likely heavy Higgs decay, $H^\mp\to tb\to b\bar b W^\mp$, and to the
irreducible background from top pair production. We find that the semi-leptonic
signature `$b\bar b W^+W^-\to b\bar b jj \ell$ + missing momentum' is dominated
by top-antitop events, which overwhelm the charged Higgs signal over the heavy
mass range that can be probed at the CERN collider
