Moving interferers with different speeds create different bearing rates while crossing the resolution cells of a uniform linear array. The notches in MVDR's beampattern do not track moving interferers well. One approach to handle this problem is to make a broader and flatter notch by applying a Covariance Matrix Taper (CMT). The CMT increases the notch width by a fixed amount at each interferer location. In practice, the bearing rate of a moving interferer is unknown and may also change over time. Different bearing rates will require different notch widths and a single fixed CMT width will not be able to suppress all moving interferers perfectly. The need for different notch widths leads us to the possibility of designing a universal adaptive beamformer for the notch width. This paper processes data from a microphone array to demonstrate that the proposed universal CMT algorithm rivals the performance of the best fixed notch width CMT beamformer in a set.