Signal from fat is normally removed from MR images either by fat separation techniques that distinguish water from fat signal after the data has been received, or by fat suppression techniques that prevent the fat signal from being received. Most approaches to fat separation are variations on Dixon imaging. The primary downside to Dixon imaging is the requirement for multiple images with stationary anatomy, often with specific TEs. An alternate approach is to take only one image, estimate phase errors to correct for inhomogeneity or other effects, and then separate the water and fat using the known phase shift. This has shown promise in previously published work, but the water and fat signals were always perpendicular, requiring a fixed TE. We consider the possibility of separation from a single, phase-corrected image with an arbitrary angle between water and fat signals. We note that a change of basis will separate water and fat signals into two images with additive zero-mean Gaussian noise. However, as the angle between water and fat nears pi or 0, the noise power in the separated images increases rapidly. We discuss techniques for reducing this noise magnification.