Improved compression of ultrasound images is highly desirable for real-time medical imaging systems. In this work we propose a novel compression method for ultrasound images. Ultrasonic images are modeled as a sum of brighter areas, termed strong reflectors, of speckle noise and of underlying tissue pattern. We then apply a combined scheme of strong reflectors segmentation and separation, and an optional speckle noise filtering. The strong reflectors are detected and interpolated using a Markov model, whilst the speckle filtering is applied using a wavelet multiresolution decomposition. The image is then compressed using a Discrete Cosine or Wavelet transform. Our new approach allows control of the speckle components intensity; for the case of strong reflectors separation with no speckle filtering, experiments with real images yield improved Rate-Distortion Curves compared to existing methods. If in addition speckle filtering is applied, a significant visual enhancement of the images is obtained.