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In freehand elastography, the ultrasound probe is moved to compress the tissue while RF-data are acquired. The axial strain tensor is estimated by calculating the gradient of the axial displacement occurring after a quasi-static tissue compression. For a given elastography frame-rate (FE), the compression speed must be appropriate to avoid the displacement between two frames being either too small or too large to be reliably estimated. The purpose of this paper is twofold. The first goal is to show that it is possible to obtain robust displacement information by calculating the echo phase shift in the Fourier domain. Second, we investigate the potential advantages of high frame-rate imaging in this field. Experimental results obtained with the ULtrasound Advanced Open Platform (ULA-OP) show that the Fourier-based method is robust over a wide FE range and that the high frame-rate imaging method allows to increase the elastograms quality, in terms of non uniformity level.