A Bayesian estimator has been developed as a paradigm for human observer performance in detecting lesions of unknown size in a uniform noisy background. The Bayesian observer used knowledge of the range of possible lesion sizes as a prior; its predictions agreed well with the results of a six‐observer perceptual study. The average human response to changes in collimator resolution, as measured by the detectability index,dA, was tracked by the Bayesian detector's signal‐to‐noise ratio (SNR) somewhat better than by two other estimation models based, respectively, on lesser and greater degrees of lesion size uncertainty. As the range of possible lesion sizes increased, the Bayesian detector's SNR decreased and the optimal collimator resolution shifted towards better resolution. An analytic approximation for the variance of lesion activity estimates (which included the same prior) was shown to predict the variance of the Bayesian estimator over a wide range of collimator resolution values. Because the bias of the Bayesian estimator was small (<1%), the analytic variance estimate permitted a rapid and convenient prediction of the Bayesian detection SNR. This calculation was then used to optimize the geometric parameters of a two‐layer tungsten collimator being constructed from crossed grids for a new imaging detector. A Monte Carlo program was first run to estimate all contributions to the radial point‐spread function for collimators of differing tungsten contents and spatial resolution values, imaging 140‐keV photons emitted from the center of a 15‐cm‐diameter, water‐filled attenuator. The optimal collimator design for detecting lesions with unknown diameters in the range 2.5–7.5 mm yielded a system resolution of ∼8.5‐mm FWHM, a geometric collimator efficiency of 1.21×10−4, and a single‐septum penetration probability of 1%.