In this paper we discuss a general framework for analysing labour supply behaviour in the presence of complicated budget and quantity constraints, of which some are unobserved. The individual's labour supply decision is viewed as a choice from a set of discrete alternatives (jobs). These jobs are characterized by attributes such as hours of work, sector-specific wages and other sector-specific aspects of the jobs. The labour supply model for married women is estimated on Norwegian data. Wage elasticities and the outcome of a tax reform experiment show that overall labour supply is moderately elastic, but these modest overall responses shadow for much stronger inter-sectoral changes. Our model is compared with a discrete choice model in which the utility is assumed to be a polynomial. We show that our estimated model has a more economically sensible interpretation and fits the data as well as the alternative approach.