In modern computed tomography (CT) there is a strong desire to reduce patient dose and/or to improve image quality by increasing spatial resolution and decreasing image noise. These are conflicting demands since increasing resolution at a constant noise level or decreasing noise at a constant resolution level implies a higher demand on x-ray power and an increase of patient dose. X-ray tube power is limited due to technical reasons. We therefore developed a generalized multi-dimensional adaptive filtering approach that applies nonlinear filters in up to three dimensions in the raw data domain. This new method differs from approaches in the literature since our nonlinear filters are applied not only in the detector row direction but also in the view and in the z-direction. This true three-dimensional filtering improves the quantum statistics of a measured projection value proportional to the third power of the filter size. Resolution tradeoffs are shared among these three dimensions and thus are considerably smaller as compared to one-dimensional smoothing approaches. Patient data of spiral and sequential single- and multi-slice CT scans as well as simulated spiral cone-beam data were processed to evaluate these new approaches. Image quality was assessed by evaluation of difference images, by measuring the image noise and the noise reduction, and by calculating the image resolution using point spread functions. The use of generalized adaptive filters helps to reduce image noise or, alternatively, patient dose. Image noise structures, typically along the direction of the highest attenuation, are effectively reduced. Noise reduction values of typically 30%-60% can be achieved in noncylindrical body regions like the shoulder. The loss in image resolution remains below 5% for all cases. In addition, the new method has a great potential to reduce metal artifacts, e.g., in the hip region.