Innovations in stream configuration operations and playback operations for adaptive streaming of panoramic video are described. The innovations include features of adaptive streaming of panoramic video with composite pictures. For example, a stream configuration tool splits an input picture of panoramic video into multiple sections and creates multiple composite pictures. A composite picture includes one of the sections as well as a low-resolution version of the input picture. A playback tool reconstructs one or more composite pictures. Under normal operation, the playback tool can use the reconstructed section(s) of the composite picture(s) to render high-quality views of the panoramic video. If the view window dramatically changes, however, or if encoded data for a section is lost or corrupted, the playback tool can use the low-resolution version of the input picture to render lower-quality details for views of the panoramic video, without disruption of playback.