  We analyse the general boundary conditions (branes) consistent with the
Poisson-sigma model and study the structure of the phase space of the model
defined on the strip with these boundary conditions. Finally, we discuss the
perturbative quantization of the model on the disc with a Poisson-Dirac brane
and relate it to Kontsevich's formula for the deformation quantization of the
Dirac bracket induced on the brane.
