An acoustic telemetry system is disclosed that reduces any through-drillstring drilling noise which contaminates a through-drillstring telemetry signal. Normal filtering operations are provided to remove noise outside the frequency band of interest, and reference signal filtering operations are provided to reduce the in-band noise, thereby enhancing the telemetry system's data rate and reliability. In one embodiment, the acoustic telemetry system includes a transmitter and a receiver. The transmitter induces an acoustic information signal that propagates along the tubing string. Existing noise in the tubing string contaminates the information signal. The receiver is provided with sensors for measuring the corrupted information signal and a reference signal that is indicative of the noise present in the measured information signal. The receiver uses a filter to convert the reference signal into an estimate of the information signal corruption, and a summing element to subtract the estimate from the reference signal to produce an information signal with reduced corruption. In a preferred embodiment, the information signal is propagated in an axial transmission mode, and the noise in the torsional mode is used as the reference signal for reducing noise the information signal picks up in the axial mode.