The paper studies the problem of learning a mixture of well-separated Gaussians under a DP constraint. This is a basic ML task and studying DP versions of it is natural. The current work gives a Differentially Private version of a simple spectral algorithm of Achlioptas and McSherry. This authors show that their algorithm has a very small sample complexity overhead for a large range of parameters. This improves on previous work on this problem, and the reviewers found the techniques to be interesting.