The success of neural networks comes hand in hand with a desire for more interpretability. We focus on text classifiers and make them more interpretable by having them provide a justification–a rationale–for their predictions. We approach this problem by jointly training two neural network models: a latent model that selects a rationale (i.e. a short and informative part of the input text), and a classifier that learns from the words in the rationale alone. Previous work proposed to assign binary latent masks to input positions and to promote short selections via sparsity-inducing penalties such as L0 regularisation. We propose a latent model that mixes discrete and continuous behaviour allowing at the same time for binary selections and gradient-based training without REINFORCE. In our formulation, we can tractably compute the expected value of penalties such as L0, which allows us to directly optimise the model towards a pre-specified text selection rate. We show that our approach is competitive with previous work on rationale extraction, and explore further uses in attention mechanisms.