This paper proposes an econometric methodology for estimating the conditional probability of an individual leaving unemployment in any particular week of his spell out of work. We use this method with cross-section data on uncompleted unemployment spells to investigate a number of questions concerning unemploymentduration. In particular we look at the impact of unemployment benefits and how this changes over the course of an unemployment spell. We also consider how our results are affected by unobserved sample heterogeneity and present estimates which, to some extent, take account of this problem.