  The problem of absence of eigenvalues imbedded into the continuous spectrum
is considered for a Schr\"{o}dinger operator with a periodic potential
perturbed by a sufficiently fast decaying ``impurity'' potential. Results of
this type have previously been known for the one-dimensional case only. Absence
of embedded eigenvalues is shown in dimensions two and three if the
corresponding Fermi surface is irreducible modulo natural symmetries. It is
conjectured that all periodic potentials satisfy this condition. Separable
periodic potentials satisfy it, and hence in dimensions two and three
Schr\"{o}dinger operator with a separable periodic potential perturbed by a
sufficiently fast decaying ``impurity'' potential has no embedded eigenvalues.
