The problem of negative artifacts in emission tomography reconstructions computed by filtered backprojection (FBP) is of practical concern particularly in low count studies. Statistical reconstruction methods based on maximum likelihood (ML) are automatically constrained to be non-negative but their excessive computational overhead (orders of magnitude greater than FBP) has limited their use in operational settings. Motivated by the statistical character of the negativity artifact, the authors develop a simple post-processing technique that iteratively adjusts negative values by cancellation with positive values in a surrounding local neighborhood. The compute time of this approach is roughly equivalent to 2 applications of FBP. The approach was evaluated by numerical simulation in 1- and 2-dimensional (2D) settings. In 2D, the source distributions included the Hoffman, the Shepp and Vardi, and a digitized version of the Jaszczak cold spheres phantoms. The authors' studies compared smoothed versions of FBP, the post-processed FBP, and ML implemented by the expectation-maximization algorithm. The root mean square (RMS) error between the true and estimated source distribution was used to evaluate performance; in 2D, additional region-of-interest-based measures of reconstruction accuracy were also employed. In making comparisons between the different methods, the amount of smoothing applied to each reconstruction method was adapted to minimize the RMS error-this was found to be critical.