We present a simple approach for producing a small number of structured visual outputs which have high recall, for a variety of tasks including monocular pose estimation and semantic scene segmentation. Current state-of-the-art approaches learn a single model and modify inference procedures to produce a small number of diverse predictions. We take the alternate route of modifying the learning procedure to directly optimize for good, high recall sequences of structured-output predictors. Our approach introduces no new parameters, naturally learns diverse predictions and is not tied to any specific structured learning or inference procedure. We leverage recent advances in the contextual submodular maximization literature to learn a sequence of predictors and empirically demonstrate the simplicity and performance of our approach on multiple challenging vision tasks including achieving state-of-the-art results on multiple predictions for monocular pose-estimation and image foreground/background segmentation.