  The \emph{Bohr compactification} of an arbitrary topological group $G$ is
defined as the group compactification $(bG,b)$ with the following universal
property: for every continuous homomorphism $h$ from $G$ into a compact group
$K$ there is a continuous homomorphism $h^{b}$ from $bG$ into $K$ extending $h$
in the sense that $h=h^b \circ b$. The Bohr compactification $(bG,b)$ is the
unique (up to equivalence) largest compactification of $G$. Although, for
locally compact Abelian groups, the Bohr compactification is a big monster, for
non-Abelian groups the situation is much more interesting and it can be said
that all options are possible. Here we are interested in locally compact groups
whose Bohr compactification is \emph{small}. Among other results, we
characterize when the Bohr the Bohr compactification of a locally compact group
is topologically isomorphic to its Chu or unitary quasi-dual. Our results fixe
some incorrect statements appeared in the literature.
