  We present fixed-$t$ subtracted dispersion relations for Compton scattering
off the nucleon at energies $E_\gamma \leq$ 500 MeV, as a formalism to extract
the nucleon polarizabilities with a minimum of model dependence. The subtracted
dispersion integrals are mainly saturated by $\pi N$ intermediate states in the
$s$-channel $\gamma N \to \pi N \to \gamma N$ and $\pi \pi$ intermediate states
in the $t$-channel $\gamma \gamma \to \pi \pi \to N \bar N$. For the subprocess
$\gamma \gamma \to \pi \pi$, we construct a unitarized amplitude and find a
good description of the available data. We show results for Compton scattering
using the subtracted dispersion relations and display the sensitivity on the
scalar polarizability difference $\alpha - \beta$ and the backward spin
polarizability $\gamma_\pi$, which enter directly as fit parameters in the
present formalism.
