Two distinctly different methods have been used to improve images produced in positron-emission tomography. The first method is to measure the differential time of flight of the photon pairs which are detected; the second is to use an iterative algorithm which computes maximum-likelihood estimates of radioactivity distributions. We have quantified the performance of algorithms which include neither, one or the other, or both methods of improvement by performing a repetitive simulation experiment using the Hoffman brain phantom as the underlying distribution of radioactivity. Our simulations show that all of the algorithms yield unbiased estimates of the desired image. The algorithm which computes maximum-likelihood estimates using time-of-flight information reconstructs images with the lowest variance. The algorithm which uses neither of these methods (filtered backprojection) reconstructs images with the highest variance.