The line-space hierarchy is a very powerful approach for the efficient update of radiosity solutions accrding to geometry changes. However, it suffers from its enormous memory consumption when storing shafts for the entire scene. We propose a method for reducingthe memory requirements of the line-space hierarchy by the dynamic management of shaft storage. We store shaft information only locally for those parts of the scene that are currently affected by the geometry change. When the dynamic object enters new regions, new shaft data has to be computed, but on the other hand we can get rid of outdated data 'behind' the dynamic object. Simple movement prediction schemes are applied, so that we can provide shaft data to the radiosity update process in time when needed. We show how storage management and pre-calculation of shafts can be efficiently performed in parallel to the radiosity update process itself.