  Most limits on the fourth generation heavy top quark (the t') are based on
the assumed dominance of t' -> Wb, which is expected to be case in the minimal
fourth generation framework with a single Higgs (the so called SM4). Here we
show, within a variant of a Two Higgs Doublet Model with four generations of
fermions, that, in general, a different t' detection strategy is required if
the physics that underlies the new heavy fermionic degrees of freedom goes
beyond the "naive" SM4. We find that the recent CMS lower bounds: m_{t'}< 450
GeV in the semi-leptonic channel pp -> t't' -> l\nu qqbb and m_{t'}< 557 GeV in
the dilepton channel pp -> t't' ->ll\nu \nu bb, that were obtained using the
customary (SM4-driven) detection strategies, do not apply. In particular, we
demonstrate that if the decay t' -> ht dominates, then applying the "standard"
CMS search tools leads to a considerably relaxed lower bound: m_{t'} >~350 GeV.
We, therefore, suggest an alternative search strategy that is more sensitive to
beyond SM4 dynamics of the fourth generation fermions.
