  We conjecture (analytically) and demonstrate (numerically) the existence of a
fine-structure above the power-law behavior of the mass of black-holes that
form in gravitational collapse of spherical massless scalar field. The
fine-structure is a periodic function of the critical-separation $(p-p^*)$. We
predict that the period $\varpi$ is {\it universal} and that it depends on the
previous universal parameters, the critical exponent, $\beta$, and the echoing
period $\Delta$ as $\varpi = \Delta /\beta$.
