This talk will be about joint work with Fabian Ziltener in which we show that a compact n-rectifiable subset of R^2n with vanishing n-Hausdorff measure can be displaced from itself by a Hamiltonian diffeomorphism arbitrarily close to the identity. This has the consequence that such a set can be arbitrarily symplectically squeezed, i.e. embedded into any neighborhood of the origin in R^2n