Multimode polymer waveguides are promising for use in board-level optical interconnects. In recent years, various on-board optical interconnection architectures have been demonstrated making use of passive routing waveguide components. In particular, 90 bends have played important roles in complex waveguide layouts enabling interconnection between non co-linear points on a board. Due to the dimensions and index step of the waveguides typically used in on-board optical interconnects, low-loss bends are typically limited to a radius of 10 mm. This paper therefore presents the design and fabrication of compact low-loss waveguide bends with reduced radii of curvature, offering significant reductions in the required areas for on-board optical circuits. The proposed design relies on the exposure of the bend section to the air, achieving tighter light confinement along the bend and reduced bending losses. Simulation studies carried out with ray tracing tools and experimental results from polymer samples fabricated on FR4 are presented. Low bending losses are achieved from the air-exposed bends up to 4 mm of radius of curvature, while an improvement of 14 m in the 1 dB alignment tolerances at the input of these devices (fibre to waveguide coupling) is also obtained. Finally, the air-exposed bends are employed in an optical bus structure, offering reductions in insertion loss of up to 3.8 dB. Index Terms-Board-level optical interconnects, multimode waveguide bends, polymer waveguides.