An approach to physical mapping is analyzed here. This procedure consists of fingerprinting random clones with single-copy landmarks extracted randomly from a region of interest. Results are presented in terms of number of contigs (sets of overlapping clones), number of isolated clones, average length of a contig, and coverage of the genome by contigs larger than a given size. (i) The expected results of an ideal project are presented. (ii) Certain problems that could influence progress of the map (variability in clone insert length, double inserts, etc.) are considered. (iii) An optimal project, which consists of a 7-fold representative library fingerprinted with an average of five sequence-tagged sites per clone, is analyzed. (iv) We present strategical considerations for the proposed approach, and a strategy that minimizes the number of laboratory tests without significant information loss is proposed: clones are arranged on a matrix and pooled according to rows and columns. A fingerprint is determined for each pool, and analysis allows retrieval of the positive clones. This method reduces the number of laboratory tests done by a factor of 160.