  We establish global regularity for the logarithmically energy-supercritical
wave equation $\Box u = u^5 \log(2+u^2)$ in three spatial dimensions for
spherically symmetric initial data, by modifying an argument of Ginibre, Soffer
and Velo \cite{gsv} for the energy-critical equation. This example demonstrates
that critical regularity arguments can penetrate very slightly into the
supercritical regime.
