A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1−s2)1/2 on [−1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L∞, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern [‘‘Well-posedness of one-way wave equations and absorbing boundary conditions,’’ Math. Comput. 47, 421–435 (1986)].