  Let $T_n$ denote the binary tree of depth $n$ augmented by an extra edge
connected to its root. Let $C_n$ denote the cover time of $T_n$ by simple
random walk. We prove that $\sqrt{ \mathcal{C}_{n} 2^{-(n+1) } } - m_n$
converges in distribution as $n\to \infty$, where $m_n$ is an explicit
constant, and identify the limit.
