Increasingly, three-dimensional (3-D) imaging technologies are used in medical diagnosis, for therapy planning, and during interventional procedures. We describe the possibilities of fast 3-D-reconstruction of high-contrast objects with high spatial resolution from only a small series of two-dimensional (2-D) planar radiographs. The special problems arising from the intended use of an open, mechanically unstable C-arm system are discussed. For the description of the irregular sampling geometry, homogeneous coordinates are used thoroughly. The well-known Feldkamp algorithm is modified to incorporate corresponding projection matrices without any decomposition into intrinsic and extrinsic parameters. Some approximations to speed up the whole reconstruction procedure and the tradeoff between image quality and computation time are also considered. Using standard hardware the reconstruction of a 256(3) cube is now possible within a few minutes, a time that is acceptable during interventions. Examples for cranial vessel imaging from some clinical test installations will be shown as well as promising results for bone imaging with a laboratory C-arm system.