A method for the rapid tracing of polypeptide backbones has been developed. The method creates an approximate chain tracing that is useful for visual evaluation of whether a structure has been solved and for use in scoring the quality of electron-density maps. The essence of the method is to (i) sample candidate C(alpha) positions at spacings of approximately 0.6 A along ridgelines of high electron density, (ii) list all possible nonapeptides that satisfy simple geometric and density criteria using these candidate C(alpha) positions, (iii) score the nonapeptides and choose the highest scoring ones, and (iv) find the longest chains that can be made by connecting nonamers. An indexing and storage scheme that allows a single calculation of most distances and density values is used to speed up the process. The method was applied to 42 density-modified electron-density maps at resolutions from 1.5 to 3.8 A. A total of 21 428 residues in these maps were traced in 24 CPU min with an overall r.m.s.d. of 1.61 A for C(alpha) atoms compared with the known refined structures. The method appears to be suitable for rapid evaluation of electron-density map quality.