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We outline a strategy to efficiently include the electromagnetic interactionsof the sea quarks in QCD+QED. When computing iso-spin breaking corrections tohadronic quantities at leading order in the electromagnetic coupling, thesea-quark charges result in quark-line disconnected diagrams which arechallenging to compute precisely. An analysis of the variance of stochasticestimators for the relevant traces of quark propagators helps us to improve thesituation for certain flavour combinations and space-time decompositions. Wepresent preliminary numerical results for the variances of the correspondingcontributions using an ensemble of $N_\mathrm{f}=2+1$ domain-wall fermionsgenerated by the RBC/UKQCD collaboration.

Efficiently unquenching QCD+QED at O($\alpha$)