We present a simple model of anisotropic pickup ion distributions on a flux tube containing both a radial segment and segments oriented perpendicular to the radial direction. The flux tube is carried away from the Sun by a constant speed solar wind. We model the pitch-angle scattering of these ions by a hemispherical approximation, which assumes that the scattering is instantaneous except through the pitch angle of 90¿, where the scattering is finite. The model includes a radially dependent ionization of pickup ions, with the newly created ions concentrated in the sunward hemisphere within the radial segment but distributed equally between the hemispheres in the perpendicular segments. The pickup ions stream along the magnetic field and decelerate in the expanding solar wind, but we assume that the radial segment is short enough that the effects of adiabatic focusing may be neglected. For weak scattering through 90¿, the distributions exhibit nonlocal properties due to ion streaming along the field from regions where conditions are different than observed locally. We find that this model can yield a depletion of antisunward ions in the radial segment of the flux tube, such as has been observed, but the streaming of ions into the radial region limits the size of this effect unless the radial segment is very long. ¿ 1998 American Geophysical Union