Rapid protein-structure determination relies greatly on software that can automatically build a protein model into an experimental electron-density map. In favorable circumstances, various software systems are capable of building over 90% of the final model. However, completeness falls off rapidly with the resolution of the diffraction data. Manual completion of these partial models is usually feasible, but is time-consuming and prone to subjective interpretation. Except for the N- and C-termini of the chain, the end points of each missing fragment are known from the initial model. Hence, fitting fragments reduces to an inverse-kinematics problem. A method has been developed that combines fast inverse-kinematics algorithms with a real-space torsion-angle refinement procedure in a two-stage approach to fit missing main-chain fragments into the electron density between two anchor points. The first stage samples a large number of closing conformations, guided by the electron density. These candidates are ranked according to density fit. In a subsequent refinement stage, optimization steps are projected onto a carefully chosen subspace of conformation space to preserve rigid geometry and closure. Experimental results show that fitted fragments are in excellent agreement with the final refined structure for lengths of up to 12-15 residues in areas of weak or ambiguous electron density, even at medium to low resolution.