  Let $K \subseteq \mathbb{R}^{2 \times 2}$ be a compact set, let $K^{rc}$ be
its rank-one convex hull, and let $L(K)$ be its lamination convex hull. It is
shown that the mapping $K \to \overline{L(K)}$ is not upper semicontinuous on
the diagonal matrices in $\mathbb{R}^{2 \times 2}$, which was a problem left by
Kol\'a\v{r}. This is followed by an example of a 5-point set of $2 \times 2$
symmetric matrices with non-compact lamination hull. Finally, an example of
another 5-point set $K$ is given, which has $L(K)$ connected, compact and
strictly smaller than $K^{rc}$.
