  The E1 strength is systematically analyzed in very neutron-rich Sn nuclei,
beyond $^{132}$Sn until $^{166}$Sn, within the Relativistic Quasiparticle
Random Phase Approximation. The great neutron excess favors the appearance of a
deformed ground state for $^{142-162}$Sn. The evolution of the low-lying
strength in deformed nuclei is determined by the interplay of two factors,
isospin asymmetry and deformation: while greater neutron excess increases the
total low-lying strength, deformation hinders and spreads it. Very neutron rich
deformed nuclei may not be as good candidates as stable spherical nuclei like
$^{132}$Sn for the experimental study of low-lying E1 strength.
