Computed tomography (CT) has been established as a major imaging modality in diagnostic radiology. Accordingly, acceptance testing and quality control of CT scanners is of great importance. While most procedures and phantoms for testing are widely accepted, there is still discussion and uncertainty about low-contrast (LC) sensitivity. In our opinion this unsatisfactory situation is caused at least in part by the lack of suitable phantoms for LC resolution measurements. We investigated the commonly used phantoms for LC detectability, the Catphan, and for LC resolution, the ATS phantom. While the Catphan showed stable object contrasts, the ATS phantom's measured contrast exhibited a strong dependence on temperature and x-ray quality. Based on newly developed polyurethane resin materials, we designed and tested a LC resolution phantom with several different contrast steps. The object contrasts showed no dependence on temperature and beam quality. The new LC resolution phantom proved to be very suitable for measuring a scanner's low-contrast sensitivity in the image plane, one of the most important image quality parameters. To assess LC resolution in three dimensions we designed an additional phantom with rows of spherical objects. A first prototype was evaluated in a multicenter study. The setup proved to be very helpful to quantify the in-plane and axial LC sensitivity of spiral CT scan modes.