Noise caused by and leaking from a transmit signal into a radio-frequency (RF) receive path signal is reduced by forwarding the transmit signal to a first filter or a digital processor and DAC, scaling the transmit signal and approximating the noise, subtracting first and second corrective signals from the RF receive path signal, down-converting a resulting corrected RF receive path signal, filtering the down-converted corrected signal in a second filter, up-converting the filtered corrected signal to create the first corrective signal, and up-converting the filter or DAC output signal to create the second corrective signal. The transmit signal may come from an output of an RF power amplifier, and may be down-converted prior to filtering in the first filter or processing in the digital processor. The second filter may be a series filter or a shunt filter. A radio includes the circuits to perform the above method.