  Let S^3_r(K) be the oriented 3--manifold obtained by rational r-surgery on a
knot K in S^3. Using the contact Ozsvath-Szabo invariants we prove, for a class
of knots K containing all the algebraic knots, that S^3_r(K) carries positive,
tight contact structures for every r not= 2g_s(K)-1, where g_s(K) is the slice
genus of K. This implies, in particular, that the Brieskorn spheres
-Sigma(2,3,4) and -Sigma(2,3,3) carry tight, positive contact structures. As an
application of our main result we show that for each m in N there exists a
Seifert fibered rational homology 3-sphere M_m carrying at least m pairwise
non-isomorphic tight, nonfillable contact structures.
