  We study several deformations of the Skyrme model in three dimensions with
self-dual sectors of arbitrary baryonic charge. We show that, for a family of
background metrics as well as for a family of field dependent couplings, the
model has one BPS sector, which may have any topological charge. We also study
the gravitating case, where there are infinite BPS sectors, provided that a
cosmological constant is added to the model.
