One of the goals of the Human Genome Project is to produce libraries of largely contiguous, ordered sets of molecular clones for use in sequencing and gene mapping projects. This is planned to be done for human and many model organisms. Theory and practice have shown that long-range contiguity and the degree to which the entire genome is covered by ordered clones can be affected by many biological variables. Many laboratories are currently experimenting with different experimental strategies and theoretical models to help plan strategies for accomplishing longrange molecular mapping of genomes. Here we describe a new mathematical model and formulas for helping to plan genome mapping projects, using various single-copy landmark (SCL) detection, or “anchoring”, strategies. We derive formulas that allow us to examine the effects of interactions among the following variables: average insert size of the cloning vector, average size of SCL, the number of SCL, and the redundancy in coverage of the clone library. We also examine and compare three different ways in which anchoring can be implemented: (1) anchors are selected independently of the library to be ordered (random anchoring); (2) anchors are made from end probes from both ends of clones in the library to be ordered (nonrandom anchoring); and (3) anchors are made from one end or the other, randomly, from clones in the library to be ordered (nonrandom anchoring). Our results show that, for biologically realistic conditions, nonrandom anchoring is always more effective than random anchoring for contig building, and there is little to be gained from making SCL from both ends of clones vs. only one end of clones. We compare and contrast our results with other similar mathematical models.