Using client-server session parallelism (CSSP), a client device establishes multiple network communication sessions with different remote servers and requests the same unsegmented data item from each server. Whichever copy of the unsegmented data item is received earliest at the client device is provided to an application. The CSSP software may be part of a network stack, or it may be part of a particular application such as a browser or a media player. The servers are not necessarily CSSP-aware, but when they are, sessions may be load-balanced. CSSP sessions may also be transferred to other CSSP-aware servers in view of server loads, imminent server reboots, or other events. A CSSP client may notify a CSSP server of status information describing session(s) established at the client with other server(s), allowing the server to reallocate bandwidth to other clients when the CSSP client has sufficient alternate data sources.