Tight contact structures on 3-manifolds seem to capture important differential topological information about the underlying 3-manifold. We will use contact surgery in order to construct contact structures on certain small Seifert fibered 3-manifolds and compute their contact Ozsvath-Szabo invariants in order to prove their tightness. In some cases, when coupled with convex surface theory, this approach leads to a complete classification of tight contact structures on the given 3-manifold. We will demonstrate this latter case by an example.