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In this work the level of positive bias in images generated by various iterative reconstructions of low activity PET data was investigated. A 3D acquisition of a low activity cylinder was performed upon an EXACT3D PET scanner followed by a multi-trial single plane simulation based upon this scan, taking into account randoms, scatter and attenuation. These were reconstructed using different implementations of maximum likelihood expectation maximisation, including the simple case of fully precorrected data and also using a separate randoms estimate with the shifted Poisson and prompts approaches. The effect of estimating the mean of randoms from the noisy delayed randoms with a maximum likelihood technique was also investigated.