  We update the determination of the isovector nucleon electromagnetic
self-energy, valid to leading order in QED. A technical oversight in the
literature concerning the elastic contribution to Cottingham's formula is
corrected and modern knowledge of the structure functions is used to precisely
determine the inelastic contribution. We find \delta M_{p-n}^\gamma =
1.30(03)(47) MeV. The largest uncertainty arises from a subtraction term
required in the dispersive analysis, which can be related to the isovector
magnetic polarizability. With plausible model assumptions, we can combine our
calculation with additional input from lattice QCD to constrain this
polarizability as: \beta_{p-n} = -0.87(85) x 10^{-4} fm^3.
