The design of physical compliance -- its location, degree, and structure -- affects robot performance and robustness in contact-rich tasks. While compliance is often used in the robot's joints, flange, or end-effector, this paper proposes compliant structures in the environment, allowing safe and robust contact while keeping the higher motion control bandwidth and precision of high impedance robots. Compliance is here realized with flexures and viscoelastic materials, which are integrated to several mechanisms to offer structured compliance, such as a remote center of compliance. Additive manufacturing with fused deposition modeling is used, allowing faster design iteration and low-cost integration with standard industrial equipment. Mechanical properties, including the total stiffness matrix, stiffness ratio, and rotational precision, are analytically determined and compared to experimental results. Three remote center of compliance (RCC) devices and a 1-DOF linear device are prototyped and tested in high-speed assembly tasks.