Strain is considered to be a useful indicator of atherosclerotic plaque vulnerability. This study introduces an alternative for a recently introduced strain imaging method that combined beam steered ultrasound acquisitions to construct radial strain images of transverse cross-sections of superficial arteries. In that study, axial strains were projected in the radial direction. Using the alternative method introduced in this study, axial displacements are projected radially, followed by a least squares estimation of radial strains. This enables the use of a larger projection angle. Consequently, fewer acquisitions at smaller beam steering angles are required to construct radial strain images. Simulated and experimentally obtained radio-frequency data of radially expanding vessel phantoms were used to compare the two methods. Using only three beam steering angles (-30�, 0� and 30�), the new method outperformed the older method that used seven different angles and up to 45� of beam steering: the root mean squared error was reduced by 38\% and the elastographic signal- and contrast-to-noise ratios increased by 1.8 dB and 4.9 dB, respectively. The new method was also superior for homogeneous and heterogeneous phantoms with eccentric lumens. To conclude, an improved noninvasive method was developed for radial strain imaging in transverse cross-sections of superficial arteries.