  The hadronic contributions to the muon anomalous magnetic moment and to the
shift of the electromagnetic fine structure constant at the scale of Z boson
mass are evaluated within dispersively improved perturbation theory (DPT). The
latter merges the corresponding perturbative input with intrinsically
nonperturbative constraints, which originate in the respective kinematic
restrictions. The obtained results conform with recent assessments of the
quantities on hand.
