Air trench structures for reduced-size bends in low-index contrast waveguides are proposed. To minimize junction loss, the structures are designed to provide adiabatic mode shaping between low- and high-index contrast regions, which is achieved by the introduction of "cladding tapers." Drastic reduction in effective bend radius is predicted. We present two-dimensional (2-D) finite-difference time-domain/effective index method simulations of bends in representative silica index contrasts. We also argue that substrate loss, while present, can be controlled with such air trenches and reduced to arbitrarily low levels limited only by fabrication capabilities. The required trench depth, given an acceptable substrate loss, is calculated in three dimensions using an approximate equivalent current sheet method and also by a numerical solver for full-vector leaky modes. A simple, compact waveguide T-splitter using air trench bends is presented.