Ultrasound images are very noisy. Along with system noise, a significant noise source is the speckle phenomenon caused by interference in the viewed object. Most of the past approaches for denoising ultrasound images essentially blur the image and they do not handle attenuation. We discuss an approach that does not blur the image and handles attenuation. It is based on frequency compounding, in which images of the same object are acquired in different acoustic frequencies and, then, compounded. Existing frequency compounding methods have been based on simple averaging, and have achieved only limited enhancement. The reason is that the statistical and physical characteristics of the signal and noise vary with depth, and the noise is correlated between acoustic frequencies. Hence, we suggest two spatially varying frequency compounding methods, based on the understanding of these characteristics. As demonstrated in experiments, the proposed approaches suppress various noise sources and also recover attenuated objects while maintaining a high resolution.