  A list assignment $L$ for a graph $G$ is an $(\ell,k)$-list assignment if
$|L(v)|\geq \ell$ for each $v \in V(G)$ and $|L(u) \cap L(v)| \leq k$ for each
$uv \in E(G)$. We say $G$ is $(\ell,k)$-choosable if it admits an $L$-colouring
for every $(\ell, k)$-list assignment $L$. We prove that if $G$ is a planar
graph with $(4,2)$-list assignment $L$ and for every triangle $T \subseteq G$
we have that $|\bigcap_{v \in V(T)} L(v)| \neq 2$, then $G$ is $L$-colourable.
In fact, we prove a slightly stronger result: if $G$ contains a clique $H$ such
that $V(H) \cap V(T) \neq \emptyset$ for every triangle $T \subseteq G$ with
$|\bigcap_{v \in V(T)} L(v)| = 2$, then $G$ is $L$-colourable. Additionally, we
give a counterexample to the correspondence colouring analogue of
$(4,2)$-choosability for planar graphs.
