In this paper, we study metrics of negative type, which are metrics (V, \d) such that \sqrt{\d} is an Euclidean metric; these metrics are thus also known as "\ell_2-squared" metrics. We show how to embed n-point negative-type metrics into Euclidean space \ell_2 with distortion D = O(\log^{3/4} n). This embedding result, in turn, implies an O(\log^{3/4} k)-approximation algorithm for the Sparsest Cut problem with non-uniform demands. Another corollary we obtain is that n-point subsets of \ell_1 embed into \ell_2 with distortion O(\log^{3/4} n).