Dipole excitations below the neutron threshold in neutron-rich Sn isotopes are studied theoretically in the Quasiparticle–Phonon Model with Hartree–Fock–Bogoliubov single-particle input. Of special interest are the low-lying two-phonon 1− states and the Pygmy Dipole Resonance (PDR). The evolution of low-energy dipole excitations with neutron excess is investigated over the Sn isotopic chain including the experimentally unknown regions close to 132Sn. A dependence of the PDR strengths and centroid energies on the neutron skin thickness is found. Despite significant multi-phonon contributions to mean energies and transition strengths, the PDR states retain their one-phonon character. The fragmentation pattern is reduced with increasing neutron excess towards the N=82 shell closure which will be of advantage for future experimental work.