Many optical systems are used for specific tasks such as classification. Of these systems, the majority are designed to maximize image quality for human observers. However, machine learning classification algorithms do not require the same data representation used by humans. We investigate the compressive optical systems optimized for a specific machine sensing task. Two compressive optical architectures are examined: an array of prisms and neutral density filters where each prism and neutral density filter pair realizes one datum from an optimized compressive sensing matrix, and another architecture using conventional optics to image the aperture onto the detector, a prism array to divide the aperture, and a pixelated attenuation mask in the intermediate image plane. We discuss the design, simulation, and trade-offs of these systems built for compressed classification of the Modified National Institute of Standards and Technology dataset. Both architectures achieve classification accuracies within 3% of the optimized sensing matrix for compression ranging from 98.85% to 99.87%. The performance of the systems with 98.85% compression were between an F  /  2 and F  /  4 imaging system in the presence of noise.