Wavelet shrinkage schemes are applied for reducing noise in synthetic and experimental ultrasonic A-scans, using the Discrete Wavelet Transform (DWT) and a cycle-spinning (CS) implementation of Undecimated Wavelet Transform (UWT). A new wavelet-based denoising procedure, which we call Random Partial Cycle Spinning (RPCS) is presented and its performance is compared with that of DWT and a CS implementation of UWT. Three well known threshold selection rules (Universal, Minimax and Sure), with decomposition level dependent threshold selection, are used in all cases. Denoising using the UWT has previously shown a robust and usually better performance than denoising using DWT but with a much higher computational cost. In this work, it is shown that the alternative procedure RPCS provides a good robust performance, close to CS performance, but with a much lower computational cost.