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Results on the use of stationary wavelets for the removal of noise from ultrasonic A-scans, with very low signal-to-noise ratio (SNR), are presented. Both synthetic and experimental ultrasonic A-scans have been used. Synthetic ultrasonic traces have been generated using an approximate speckle model which includes frequency dependent attenuation and scattering. Ultrasonic signals acquired from a test block made of austenitic steel have also been denoised. Results obtained using a Cycle-Spinning (CS) implementation of the stationary wavelet transform are compared with those obtained using with the Discrete Wavelet Transform (DWT), using soft thresholding and two decomposition level dependent threshold selection rules (Universal and SURE). It is shown that both DWT and CS denoising procedures yield very bad results when using Universal thresholds. It is also shown that CS denoising using SURE thresholds is an effective approach to denoise ultrasonic signals with low initial SNR, providing very good results for both synthetic and experimental A-scans.