In this paper, we analyze firm demand for flexible jobs by exploiting the language used to describe work arrangements in job vacancies. We take a supervised machine learning approach to classify the work arrangements described in more than 46 million UK job vacancies. We highlight the existence of very different types of flexibility amongst low and high wage vacancies. Job flexibility at low wages is more likely to be offered alongside a wage-contract that exposes workers to earnings risk, while flexibility at higher wages and in more skilled occupations is more likely to be offered alongside a fixed salary that shields workers from earnings variation. We show that firm demand for flexible work arrangements is partly driven by a desire to reduce labor costs; we find that a large and unexpected change to the minimum wage led to a 7 percentage point increase in the proportion of flexible and non-salaried vacancies at low wages.