  Reconstruction problems have been studied in a number of contexts including
biology, information theory and and statistical physics. We consider the
reconstruction problem for random $k$-colourings on the $\Delta$-ary tree for
large $k$. Bhatnagar et. al. showed non-reconstruction when $\Delta \leq
\frac12 k\log k - o(k\log k)$ and reconstruction when $\Delta \geq k\log k +
o(k\log k)$. We tighten this result and show non-reconstruction when $\Delta
\leq k[\log k + \log \log k + 1 - \ln 2 -o(1)]$ and reconstruction when $\Delta
\geq k[\log k + \log \log k + 1+o(1)]$.
