  We study cosmetic contact surgeries along transverse knots in the standard
contact 3-sphere, i.e. contact surgeries that yield again the standard contact
3-sphere. The main result is that we can exclude non-trivial cosmetic contact
surgeries along all transverse knots not isotopic to the transverse unknot with
self-linking number -1. As a corollary it follows that every transverse knot in
the standard contact 3-sphere is determined by the contactomorphism type of its
exteriors. Moreover, we give counterexamples to this for transverse links in
the standard contact 3-sphere.
