The dipole strength distribution above the one-neutron separation energy was measured in the unstable 130Sn and the double-magic 132Sn isotopes. The results were deduced from Coulomb dissociation of secondary Sn beams with energies around 500 MeV/nucleon, produced by in-flight fission of a primary 238U beam. In addition to the giant dipole resonance, a resonancelike structure ("pygmy resonance") is observed at a lower excitation energy around 10 MeV exhausting a few percent of the isovector E1 energy-weighted sum rule. The results are discussed in the context of a predicted new dipole mode of excess neutrons oscillating out of phase with the core nucleons.