  Quantum electrodynamics has been the first theory to emerge from the ideas of
regularization and renormalization, and the coupling of the fermions to the
virtual excitations of the electromagnetic field. Today, bound-state quantum
electrodynamics provides us with accurate theoretical predictions for the
transition energies relevant to simple atomic systems, and steady theoretical
progress relies on advances in calculational techniques, as well as numerical
algorithms. In this brief review, we discuss one particular aspect connected
with the recent progress: the evaluation of relativistic corrections to the
one-loop bound-state self-energy in a hydrogenlike ion of low nuclear charge
number, for excited non-S states, up to the order of alpha (Zalpha)^6 in units
of the electron mass. A few details of calculations formerly reported in the
literature are discussed, and results for 6F, 7F, 6G and 7G states are given.
