  A Kakeya set $\mathcal{K}$ in an affine plane of order $q$ is the point set
covered by a set $\mathcal{L}$ of $q+1$ pairwise non-parallel lines. Large
Kakeya sets were studied by Dover and Mellinger; in [6] they showed that Kakeya
sets with size at least $q^2-3q+9$ contain a large knot (a point of
$\mathcal{K}$ lying on many lines of $\mathcal{L}$). In this paper, we improve
on this result by showing that Kakeya set of size at least $\approx
q^2-q\sqrt{q}+\frac{3}{2}q$ contain a large knot. Furthermore, we obtain a
sharp result for planes of square order containing a Baer subplane.
