  We prove that every Legendrian knot in the tight contact structure of the
3-sphere is determined by the contactomorphism type of its exterior. Moreover,
by giving counterexamples we show this to be not true for Legendrian links in
the tight 3-sphere. On the way a new user-friendly formula for computing the
Thurston-Bennequin invariant of a Legendrian knot in a surgery diagram is
given.
