  We investigate two-loop higher-order binding corrections to the fine
structure, which contribute to the spin-dependent part of the Lamb shift. Our
calculation focuses on the so-called ``two-loop self-energy'' involving two
virtual closed photon loops. For bound states, this correction has proven to be
notoriously difficult to evaluate. The calculation of the binding corrections
to the bound-state two-loop self-energy is simplified by a separate treatment
of hard and soft virtual photons. The two photon-energy scales are matched at
the end of the calculation. We explain the significance of the mathematical
methods employed in the calculation in a more general context, and present
results for the fine-structure difference of the two-loop self-energy through
the order of $\alpha^8$.
