A modem for interconnecting a DSL line and a local bus comprises a DSL interface adapted to send and receive data on the DSL line at a DSL bandwidth selected from a first set of bandwidths, and a local bus interface adapted to operate at a local bus bandwidth selected from a second set of bandwidths so as to match the DSL bandwidth. In a first operating mode, the modem reserves as much as possible of a predetermined local bus bandwidth and then synchronizes the DSL line to a matching mode. In a second operating mode, the modem synchronizes the DSL line to a predetermined bandwidth and then reserves a matching local bus bandwidth or, if impossible, adopts a bulk transfer mode.