We study the problem of classifying Legendrian knots in overtwisted contact structures on S 3. The question is whether topologically isotopic Legendrian knots have to be Legendrian isotopic if they have equal values of the well-known invariants rot and tb. We give positive answer in the case that there is an overtwisted disc intersecting none of the knots and we construct an example of a knot intersecting each overtwisted disc (this provides a counterexample to the conjecture of Eliashberg). Our proof needs some results on the structure of the group of contactomorphisms of S 3. We divide the subgroup Cont+(S 3, ξ) of coorientation-preserving contactomorphisms for an overtwisted contact distribution ξ into two classes.