  The first fully relativistic, rigorous QED calculations of the self-energy
correction to the fine-structure levels of heavy muonic atoms are reported. We
discuss nuclear model and parameter dependence for this contribution as well as
numerical convergence issues. The presented results show sizable disagreement
with previously reported estimations, including ones used for the determination
of the nuclear root-mean-square radii, and underline the importance of rigorous
QED calculations for the theoretical prediction of the spectra of muonic atoms.
