  We develop the formalism to provide an improved estimate for the hadronic
light-by-light correction to the muon's anomalous magnetic moment a_{\mu}, by
considering single meson contributions beyond the leading pseudo-scalar mesons.
We incorporate available experimental input as well as constraints from
light-by-light scattering sum rules to estimate the effects of axial-vector,
scalar, and tensor mesons. We give numerical evaluations for the hadronic
light-by-light contribution of these states to a_{\mu}. The presented formalism
allows to further improve on these estimates, once new data for such meson
states will become available.
