  We introduce a kinetically constrained spin model with a local softness
parameter, such that spin flips can violate the kinetic constraint with an
(annealed) site-dependent rate. We show that adding MC swap moves to this model
can dramatically accelerate structural relaxation. We discuss the connection of
this observation with the fact that swap moves are also able to accelerate
relaxation in structural glasses. We analyse the rates of relaxation in the
model. We also show that the extent of dynamical heterogeneity is strongly
suppressed by the swap moves.
