This paper focuses on resolving long-standing limitations of parallax barriers by applying formal optimization methods. We consider two generalizations of conventional parallax barriers. First, we consider general two-layer architectures, supporting high-speed temporal variation with arbitrary opacities on each layer. Second, we consider general multi-layer architectures containing three or more light-attenuating layers. This line of research has led to two new attenuation-based displays. The High-Rank 3D (HR3D) display contains a stacked pair of LCD panels; rather than using heuristically-defined parallax barriers, both layers are jointly-optimized using low-rank light field factorization, resulting in increased brightness, refresh rate, and battery life for mobile applications. The Layered 3D display extends this approach to multi-layered displays composed of compact volumes of light-attenuating material. Such volumetric attenuators recreate a 4D light field when illuminated by a uniform backlight. We further introduce Polarization Fields as an optically-efficient and computationally efficient extension of Layered 3D to multi-layer LCDs. Together, these projects reveal new generalizations to parallax barrier concepts, enabled by the application of formal optimization methods to multi-layer attenuation-based designs in a manner that uniquely leverages the compressive nature of 3D scenes for display applications.