A hardware-based aperture compression system permits addressing large memory spaces via a limited bus aperture. Streams are assigned dynamic base addresses (BAR) that are maintained in registers on sources and destinations. Requests for addresses lying between BAR and BAR plus the size of the bus aperture are sent with BAR subtracted off by the source and added back by the destination. Requests for addresses outside that range are handled by transmitting a new, adjusted BAR before sending the address request.