We develop an extension to the Lander-Waterman theory for characterizing gaps in bacterial artificial chromosome fingerprint mapping and shotgun sequencing projects. It supports a larger set of descriptive statistics and is applicable to a wider range of project parameters. We show that previous assertions regarding inconsistency of the Lander-Waterman theory at higher coverages are incorrect and that another well-known but ostensibly different model is in fact the same. The apparent paradox of infinite island lengths is resolved. Several applications are shown, including evolution of the probability density function, calculation of closure probabilities, and development of a probabilistic method for computing stopping points in bacterial artificial chromosome shotgun sequencing.