We demonstrate a kernel of size O(k^2) for 3-HITTING SET when all subsets in the collection to be hit are of size at most three), giving a partial answer to an open question of Niedermeier by improving on the O(k^3) kernel of Niedermeier and Rossmanith. Our technique uses the Nemhauser-Trotter linear-size kernel for vc, and generalizes to demonstrating a kernel of size O(k^{r-1}) for r- HITTING SET (for fixed r).