Three-dimensional cone-beam (CB) imaging using a multi-axis floor-mounted (or ceiling-mounted) C-arm system has become an important tool in interventional radiology. This success motivates new developments to improve image quality. One direction in which advancement is sought is the data acquisition geometry and related CB artifacts. Currently, data acquisition is performed using the circular short-scan trajectory, which yields limited axial coverage and also provides incomplete data for accurate reconstruction. To improve the image quality, as well as to increase the coverage in the longitudinal direction of the patient, we recently introduced the ellipse- line-ellipse trajectory and showed that this trajectory provides full R-line coverage within the field-of-view, which is a key property for accurate reconstruction from truncated data. An R-line is any segment of line that connects two source positions. Here, we examine how the application of asymmetrical variations to the definition of the ELE trajectory impacts the R-line coverage. This question is significant to understand how much flexibility can be used in the implementation of the ELE trajectory, particularly to adapt the scan to patient anatomy and imaging task of interest. Two types of asymmetrical variations, called axial and angular variations, are investigated.