In a stimulation study, we investigated the limitations of quantitation in nuclear medicine using a maximum-likelihood (ML) estimation model. We estimated activity, size, and position of a disk-shaped object on a circular, uniform background of unknown activity. The parameter estimates were unbiased, and their standard error was proportional to the square root of the total image counts. The estimates of object activity and size were strongly (negatively) correlated; the position estimates, however, were not correlated with estimates of any other parameters. This implies that a priori knowledge of object location does not improve precision. The minimal model of quantitation tasks should incorporate unknown object activity and size as well as unknown background activity. The ML estimation procedure was used to investigate the trade-off between resolution and sensitivity in gamma camera collimator design. The results implied that for complex tasks such as the multiparameter estimation task investigated here, optimum performance is achieved at a better resolution than that previously found optimal for detection of a well-specified object in a known background.