A new method is proposed to estimate the motion and relative local compression between two successive ultrasound RF signals under different compression states. The algorithm uses the continuous wavelet transform to locate the peaks in the RF signals. The estimated peaks in the pre- and post-compression signals are assigned to each other by a peak matching technique with the goal of minimizing the number of false matches. The method allows local shifts of the tissue to be estimated. The method has been tested in one-dimensional simulations and phantom experiments. The signal-to-noise ratio and the rms error are shown to be better than for the standard cross-correlation method (CC). The new estimator remains unbiased for up to 10% strain which is a larger range than that of CC. The maximum signal-to-noise ratio is 3 times as high as that of the CC method, showing higher sensitivity as well. The method is computationally efficient, achieving 0.7 msec/RF line on a standard personal computer.