We describe a new method for non-stationary noise suppression that is simple to implement yet has performance rivaling far more complex algorithms. Spectral Intersections is a model based MMSE signal separation method that uses a new simple approximation to the observation likelihood. Furthermore, Spectral Intersections uses an efficient approximation to the expectation integral of the MMSE estimate that could be described as unscented importance sampling. We apply the new method to the task of separating speech mixed with music. We report results on the Google Voice Search task where the new method provides a 7%% relative reduction in WER at 10dB SNR. Interestingly, the new method provides considerably greater reduction in average WER than the MAX method and approaches the performance of the more complex Algonquin algorithm.