We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver  has been improved by Sviridenko and Ward  from to k/2 + ∈ to k+2/3, and by Cygan  to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward . With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm  is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.