We study the mechanism of the phase transition between the disordered and the algebraic-ordered phases of the XY model. We use a modified Monte Carlo procedure which permits tunneling between configurations with different numbers of free vortices. The results are marginally compatible with the standard Monte Carlo. Our data do not match the predictions of the vortex liberation scenario for the topological susceptibility. We interpret these results as lack of support for the K-T picture.Bantrell Fellow.