  We present a dispersive representation of the D-term form factor for hard
exclusive reactions, using unsubtracted $t$-channel dispersion relations. The
$t$-channel unitarity relation is saturated with the contribution of two-pion
intermediate states, using the two-pion distributions amplitude for the
$\gamma^*\gamma\rightarrow \pi\pi$ subprocess and reconstructing the
$\pi\pi\rightarrow N\bar N$ subprocess from available information on
pion-nucleon partial-wave helicity amplitudes. Results for the D-term form
factor as function of $t$ as well as at $t=0$ are discussed in comparison with
available model predictions and phenomenological parametrizations.
