We studied the 2+1 dimensional XY model at nonzero chemical potential on deformed integration manifolds with the aim of alleviating
its sign problem. We investigated several proposals for the deformations and managed to considerably improve on the severity of the
sign problem with respect to standard reweighting approaches. In this talk I present numerical evidence that a significant reduction
of the sign problem can be achieved which is exponential in both the squared chemical potential and the spatial volume. Furthermore, I
discuss a new approach to the optimizaiton procedure, based on reweighting, that sensibly reduces its computational cost.