  Partial wave amplitudes of meson photoproduction reactions are an important
source of information in baryon spectroscopy. We investigate a new approach in
single-energy partial wave analyses of these reactions. Instead of using a
constraint to theoretical models in order to achieve solutions which are
continuous in energy, we enforce the analyticity of the amplitudes at fixed
values of the Mandelstam variable $t$. We present an iterative procedure with
successive fixed-$t$ amplitude analyses which constrain the single-energy
partial wave analyses and apply this method to the $\gamma p \to \eta p$
reaction. We use pseudo data, generated by the EtaMAID model, to test the
method and to analyze ambiguities. Finally, we present an analytically
constrained partial wave analysis using experimental data for four polarization
observables recently measured at MAMI and GRAAL in the energy range from
threshold to $\sqrt{s}=1.85$ GeV.
