Abstract This paper investigates several fundamental aspects of wave-permeable, or “radiation,” lateral boundary conditions. Orlanski (1976) proposed that approximate wave-permeable boundary conditions could be constructed by advecting disturbances out of the domain at a phase speed c*, which was to be calculated from the values of the prognostic variable near the boundary. Rigorous justification for this approach is possible for one-dimensional shallow-water flow. It is shown, however, that the floating c* approach gives poor results in the one-dimensional shallow-water problem because all accuracy in the c* calculations is eventually destroyed by the positive feedback between errors in c* and (initially small) errors in the prognostic fields at the boundary. Better results were achieved by using fixed values of c*. In our test cases, an externally specified c* could deviate from the true phase speed U + c by 40%–60% and still yield better results than schemes in which c* was calculated at the boundary. ...