X-ray computed laminography is widely used in nondestructive testing of relatively flat objects using an oblique scanning configuration for data acquisition. In this work, a new scanning scheme is proposed in conjunction with the compressive-sensing-based image reconstruction for reducing imaging radiation dose and scanning time. We performed a numerical study comparing image qualities acquired by various scanning configurations that are practically implementable: single-arc, double-arc, oblique, and spherical-sinusoidal trajectories. A compressive-sensing-inspired total-variation (TV) minimization algorithm was used to reconstruct the images from the data acquired at only 40 projection views in those trajectories. It was successfully demonstrated that the proposed scanning scheme outperforms the others in terms of image contrast and spatial resolution, although the oblique scanning scheme showed a comparable resolution property. We believe that the proposed scanning method may provide a solution to fast and low-dose nondestructive testing of radiation-sensitive and highly integrated devices such as multilayer microelectronic circuit boards.