Sharp bends in low index contrast waveguides using tapered air trenches are proposed. To minimize claddingtrench junction loss, "cladding tapers" are designed to provide adiabatic mode shaping between low and high index contrast regions. Drastic reduction in effective bend radius is predicted. We present 2D FDTD/EIM simulations of bends in representative silica index contrasts. Substrate loss in air trenches of finite depth is investigated, and the required trench depth, given an acceptable substrate loss, is calculated. Fabrication steps are described.