A way to make velocity estimation robust in the presence of noise is to use median stacks within CMPs. A problem with CMP stacks is that data from a large range of offsets are merged despite intrinsic variations in gain, frequency, NMO stretch, array response, and AVO. We estimate VRMS with a robust median estimator of slowness squared terms; each term manufactured from neighboring traces only. Our goal is to develop a robust code that will reasonably move out all 40 of the worldwide Yilmaz-Cumro shot profiles Yilmaz (1987) without need for individualized parameter choices.