The high resolution complete physical maps of chromosomes VII and XV were constructed to form the basis for sequencing these chromosomes as part of the European systematic sequencing programme of the yeast genome, using a unique cosmid library from strain FY1679, and an original top‐down mapping strategy involving I‐Sce I chromosome fragmentation. A total of 138 and 196 cosmid clones were used to construct the maps for VII and XV, respectively, forming two unique contigs that cover the entirety of chromosomes (1091 kb each), except the telomeric repeats. Colinearity of the cosmid inserts with yeast DNA was verified, and the physical maps were eventually compared with the independently generated genetic maps. © 1998 John Wiley & Sons, Ltd.