Dynamic attenuators are beam shaping filters that can customize the x-ray illumination field to the clinical task and for each view. These dynamic attenuators replace traditional attenuators (or "bowtie filters") and decrease radiation dose, dynamic range, and scatter when compared to their static counterparts. We propose a one-dimensional dynamic attenuator that comprises multiple wedges with axially-dependent triangular cross-sections, and which are translated in the axial direction. These wedges together produce a time-varying, piecewise-linear attenuation function. We investigate different control methods for this attenuator and estimate the ability of the dynamic attenuator to reduce dose while maintaining the peak variance of the scan. With knowledge of the patient anatomy, the dynamic attenuator can be controlled by solving a convex optimization problem. This knowledge could be determined from a low dose pre-scan. Absent this information, various heuristics can be used. We simulate the dynamic attenuator on datasets of the thorax, abdomen, and a targeted scan of an abdominal aortic aneurysm. The dose and scatter-to-primary ratio (SPR) are estimated using Monte Carlo simulations, and the noise is calculated analytically. Compared to a system using the standard bowtie with typical mA modulation, dose reductions of 50% are observed. Compared to an optimized, patientspecific mA modulation, the typical dose reduction is 30%. If the dynamic attenuator is controlled with a heuristic, typical dose reductions are also 30%. The gains are larger in the targeted scan. The SPR is also reduced by 20% in the abdomen. We conclude that the dynamic attenuator has significant potential to reduce dose without increasing the peak variance of the scan.