This paper proposes a generalization of a basic technique in differential privacy, known as the sparse vector technique. The paper offers a new style of privacy analysis for the proposed technique using Renyi Differential Privacy. The proposed technique allows for plugging in other private mechanisms as opposed to the Laplace mechanism used in the original version of the sparse vector technique. The paper also contains several experiments showing the competitiveness of the proposed technique against existing algorithms. This is an interesting result that improves and extends a basic technique in differential privacy, and could spur further work.