We propose a composite acousto-optical modulation (AOM) scheme for wide-band, efficient modulation of CW and pulsed lasers. We show that by adjusting the amplitudes and phases of weakly-driven daughter AOMs, diffraction beyond the Bragg condition can be achieved with exceptional efficiencies. Furthermore, by imaging pairs of AOMs with opposite directions of sound-wave propagation, high contrast switching of output orders can be achieved at the driving radio frequency (rf) limit, thereby enabling efficient bidirectional routing of a synchronized mode-locked laser. Here we demonstrate a simplest example of such scheme with a double-AOM setup for efficient diffraction across an octave of rf bandwidth, and for routing a mode-locked pulse train with up to frep = 400 MHz repetition rate. We discuss extension of the composite scheme toward multi-path routing and time-domain multiplexing, so as to individually shape each pulses of ultrafast lasers for novel quantum control applications.