We often explain by citing an absence or an omission. Apart from the problem of assigning a causal role to such apparently negative factors as absences and omissions, there is a puzzle as to why only some absences and omissions, out of indefinitely many, should figure in explanations. In this paper we solve this ’many absences problem’ by using the contrastive model of explanation. The contrastive model of explanation is developed by adapting Peter Lipton’s account. What initially appears to be only a trivial amendment to Lipton’s Difference Condition enables us both to offer a much more satisfactory solution to the ’many absences problem’ than David Lewis did, and also to explain why explanation in terms of absences and omissions should be so common.