  We prove that a WLD subspace of the space $\ell_\infty^c(\Gamma)$ consisting
of all bounded, countably supported functions on a set $\Gamma$ embeds
isomorphically into $\ell_\infty$ if and only if it does not contain isometric
copies of $c_0(\omega_1)$. Moreover, a subspace of $\ell_\infty^c(\omega_1)$ is
constructed that has an unconditional basis, does not embed into $\ell_\infty$,
and whose every weakly compact subset is separable (in particular, it cannot
contain any isomorphic copies of $c_0(\omega_1)$).
