A live rendering system can execute a process of buffering received data at the client to avoid needing to transfer the same data multiple times. If the client does not have data available for a wanted playback position (either compressed or decoded) then this data needs to be transferred from the server, including any overlaps needed for producing a continuous stream. The client stores the data in the event that it is needed again, but can discard the data if it receives notice that the stream content has changed. The buffering process can operate with a first priority to buffer data ahead of a currently selected playback position which is the most likely to be needed next, to minimize any delay or pauses in playback if needed data has not yet arrived. The download can be managed to preserve the known good part of decoded data.