  We give new tightness criteria for positive surgeries along knots in the
3-sphere, generalising results of Lisca and Stipsicz, and Sahamie. The main
tools will be Honda, Kazez and Matic's, Ozsvath and Szabo's Floer-theoretic
contact invariants. We compute the Ozsvath and Szabo's invariant of positive
contact surgeries along Legendrian knots in the 3-sphere in terms of the
classical invariants of the knot. We also combine a Legendrian cabling
construction with contact surgeries to get results about rational contact
surgeries.
