Many edge finders extract the signs of finite differences of image intensity values. Camera noise renders many of these signs unreliable. Previous algorithms for reducing noise are difficult to analyze, fail to detect faint or closely packed features, or are handle restricted classes of features. The author proposes taking finite differences with a range of separations between data points, and choosing the narrowest response with statistically reliable sign. Fine detail is then detected by narrow operators. Faint features are filled in by wide operators, which can more reliably distinguish low-amplitude boundaries from noise. It is shown, both theoretically and empirically, that this method out-performs traditional Gaussian smoothing. Measurements of noise in a real camera system are also presented.