  As the glass (in molecular fluids\cite{Donth}) or the jamming (in colloids
and grains\cite{LiuNature1998}) transitions are approached, the dynamics slow
down dramatically with no marked structural changes. Dynamical heterogeneity
(DH) plays a crucial role: structural relaxation occurs through correlated
rearrangements of particle ``blobs'' of size
$\xi$\cite{WeeksScience2000,DauchotPRL2005,Glotzer,Ediger}. On approaching
these transitions, $\xi$ grows in glass-formers\cite{Glotzer,Ediger},
colloids\cite{WeeksScience2000,BerthierScience2005}, and driven granular
materials\cite{KeysNaturePhys2007} alike, strengthening the analogies between
the glass and the jamming transitions. However, little is known yet on the
behavior of DH very close to dynamical arrest. Here, we measure in colloids the
maximum of a ``dynamical susceptibility'', $\chi^*$, whose growth is usually
associated to that of $\xi$\cite{LacevicPRE}. $\chi^*$ initially increases with
volume fraction $\phi$, as in\cite{KeysNaturePhys2007}, but strikingly drops
dramatically very close to jamming. We show that this unexpected behavior
results from the competition between the growth of $\xi$ and the reduced
particle displacements associated with rearrangements in very dense
suspensions, unveiling a richer-than-expected scenario.
