We study the problem of structured prediction under test-time budget constraints. We propose a novel approach applicable to a wide range of structured prediction problems in computer vision and natural language processing. Our approach seeks to adaptively generate computationally costly features during test-time in order to reduce the computational cost of prediction while maintaining prediction performance. We show that training the adaptive feature generation system can be reduced to a series of structured learning problems, resulting in efficient training using existing structured learning algorithms. This framework provides theoretical justification for several existing heuristic approaches found in literature. We evaluate our proposed adaptive system on two structured prediction tasks, optical character recognition (OCR) and dependency parsing and show strong performance in reduction of the feature costs without degrading accuracy.