In this work, we explore the potential of region-of-interest (ROI) imaging in x-ray computed tomography (CT). Using two dynamic beam attenuator (DBA) concepts for fluence field modulation (FFM) previously developed, we investigate and evaluate the potential dose savings in comparison with current FFM technology. Methods: ROI imaging is a special application of FFM where the bulk of x-ray radiation is propagated toward a certain anatomical target (ROI), specified by the imaging task, while the surrounding tissue is spared from radiation. We introduce a criterion suitable to quantitatively describe the balance between image quality inside an ROI and total radiation dose with respect to a given ROI imaging task. It accounts for the mean image variance at the ROI and the effective patient dose calculated from Monte Carlo simulations. The criterion is further used to compile task-specific DBA trajectories determining the primary x-ray fluence, and eventually used for comparing different FFM techniques, namely the sheet-based dynamic beam attenuator (sbDBA), the z-aligned sbDBA (z-sbDBA), and an adjustable static operation mode of the z-sbDBA. Furthermore, two static bowtie filters and the influence of tube current modulation (TCM) are included in the comparison. Results: Our findings demonstrate by simulations that the presented trajectory optimization method determines reasonable DBA trajectories. The influence of TCM is strongly depending on the imaging task. The narrow bowtie filter allows for dose reductions of about 10% compared to the regular bowtie filter in the considered ROI imaging tasks. The DBAs are shown to realize substantially larger dose reductions. In our cardiac imaging scenario, the DBAs can reduce the effective dose by about 30% (z-sbDBA) or 60% (sbDBA). We can further verify that the noise characteristics are not adversely affected by the DBAs. Conclusion: Our research demonstrates that ROI imaging using the presented DBA concepts is a promising technique toward a more patient-and task-specific CT imaging requiring lower radiation dose. Both the sbDBA and the z-sbDBA are potential technical solutions for realizing ROI imaging in x-ray CT.