In positron emission tomography (PET), random coincidence events must be removed from the measured signal in order to obtain quantitatively accurate data. The most widely implemented technique for estimating the number of random coincidences on a particular line of response is the delayed coincidence channel method. Estimates obtained in this way are subject to Poisson noise, which then propagates into the final image when the estimates are subtracted from the prompt signal. However, this noise may be reduced if variance reduction techniques similar to those used in normalization of PET detectors are applied to the randoms estimates prior to use. We have investigated the effects of randoms variance reduction on noise-equivalent count (NEC) rates on a whole-body PET camera operating in 3D mode. NEC rates were calculated using a range of phantoms representative of situations that might be encountered clinically. We have also investigated the properties of three randoms variance reduction methods (based on algorithms previously used for normalization) in terms of their systematic accuracy and their variance reduction efficacy, both in phantom studies and in vivo. Those algorithms investigated that do not make assumptions about the spatial distribution of random coincidences give the best estimates of the randoms distribution. With the camera used, which has a limited axial extent (10.8 cm) and a large ring diameter (102 cm), the gains in image signal-to-noise ratio obtained with this technique ranged from approximately 5% to approximately 15%, depending on object size, activity distribution and the amount of activity in the field of view. Larger gains would be expected if this technique were to be employed on cameras of greater axial extent and smaller ring diameter.