We describe a simple, novel, and efficient system for speaker comparison with two main components. First, the system uses a new approximate KL divergence distance extending earlier GMM parameter vector SVM kernels. The approximate distance incorporates data-dependent mixture weights as well as the standard MAP-adapted GMM mean parameters. Second, the system applies a weighted nuisance projection method for channel compensation. A simple eigenvector method of training is presented. The resulting speaker comparison system is straightforward to implement and is computationally simple? only two low-rank matrix multiplies and an inner product are needed for comparison of two GMM parameter vectors. We demonstrate the approach on a NIST 2008 speaker recognition evaluation task. We provide insight into what methods, parameters, and features are critical for good performance.