The problem of detecting a known signal in correlated Gaussian noise is considered. The Neyman-Pearson optimal detector for this problem is, of course, well known. Unfortunately, unless the number of observations is small, the amount of computation required to design this optimal detector can be quite substantial. For this reason, two suboptimal detectors are introduced which, for a given noise autocorrelation matrix, are much easier to design than the optimal detector. Both suboptimal detectors are based on simple modifications of the white-noise detector, and yet their performance, in many instances, is nearly optimal. In addition, a numerical study is presented which indicates that these detectors are much less sensitive to changes in the underlying noise autocorrelation function than is the Neyman-Pearson optimal detector.