  Kr\'al' and Sgall (2005) introduced a refinement of list colouring where
every colour list must be subset to one predetermined palette of colours. We
call this $(k,\ell)$-choosability when the palette is of size at most $\ell$
and the lists must be of size at least $k$. They showed that, for any integer
$k\ge 2$, there is an integer $C=C(k,2k-1)$, satisfying $C = O(16^{k}\ln k)$ as
$k\to \infty$, such that, if a graph is $(k,2k-1)$-choosable, then it is
$C$-choosable, and asked if $C$ is required to be exponential in $k$. We
demonstrate it must satisfy $C = \Omega(4^k/\sqrt{k})$.
  For an integer $\ell \ge 2k-1$, if $C(k,\ell)$ is the least integer such that
a graph is $C(k,\ell)$-choosable if it is $(k,\ell)$-choosable, then we more
generally supply a lower bound on $C(k,\ell)$, one that is super-polynomial in
$k$ if $\ell = o(k^2/\ln k)$, by relation to an extremal set theoretic
property. By the use of containers, we also give upper bounds on $C(k,\ell)$
that improve on earlier bounds if $\ell \ge 2.75 k$.
