In ultrasound elastography, axial strains of the examined tissue are calculated by the differentiation of the measured axial displacements. However, the results become obscured as high-frequency noise is amplified by the gradient operator. In this paper, we propose an advanced denoising method for axial displacements with the aim of accurately estimating their axial strains. The proposed algorithm is based on the short-term Fourier transform modified by a suitable filtering function which is able to accommodate the distinct non-stationarities present in the displacement data. Experimentation on synthetic elastograms has shown that the presented method yields accurate results and outperforms other, commonly used denoising techniques.