In the context of ultrasound (US) deformation imaging it has been shown that lateral motion estimation can be improved by simultaneously combining transverse oscillation (TO) beamforming with dedicated motion estimators and regularisation techniques. This paper provides insights into the relative contributions of beamforming strategies (focused imaging [FOC], plane wave TO beamforming [PWTO], and PWTO after heterodyning [PWTO*]) and regularisation (unregularised RF tracking, combined envelope/RF tracking without regularisation, and combined envelope/RF tracking with explicit regularisation) to the performance of US displacement estimation algorithms. More specifically, a non-rigid image registration technique was used to track lateral tissue motion in an in-silico and in-vitro phantom setup for all beamforming-tracking combinations. It was found that PWTO and PWTO* tracking benefited more from regularisation than FOC tracking, and was even a necessary requirement to warrant the use of TO beamforming over traditional FOC imaging. For example, for a range of lateral displacements (0-1000 μm), in-silico errors were 56±56 μm and 118±293 μm for the unregularized FOC and PWTO* scenario respectively. After regularisation, these errors remained relatively stable for the FOC case but drastically reduced for the PWTO* scenario: 51±45 μm versus 14±12 μm respectively.