We first describe experiments designed to measure the spatial distribution of noise within an electrical impedance tomographic image of a saline-filled tank. These experiments show that the noise increases by a factor of up to 30 from the periphery towards the centre of the image. We then propose a method of noise equalization that depends upon spending longer collecting the smaller potentials than the larger potentials. The method is tested and shown to give an improvement in noise uniformity of about 16 dB.