Many digital delta–sigma radio frequency (RF) upconverters exhibit poor performance when the carrier frequency is tuned away from the centre of the band. The offsetting of signals from the nominal carrier frequency position generates unwanted distortion products which are dominated by the image and third harmonics. It is shown that these products can be moved out of the band by the correct choice of intermediate frequency. A novel technique for shifting both the signal and the noise null to the new frequency position is described.