  We prove that two Legendrian knots in a contact structure which is
trivializable as a plane bundle are Legendrian isotopic provided that (1) they
are isotopic as framed knots, (2) they have the same rotation number with
respect to some parallelization of the contact structure, and (3) there is an
overtwisted disk disjoint with both knots. (For zero-homologous knots the
condition (1) reads as: (1a) they are isotopic as topological knots, and (1b)
they have the same Thurston-Bennequin invariant.) Then we discuss the situation
when condition (3) is not fulfilled, in particular that of non-loose Legendrian
knots.
