The goal of this work is to address the problem of quantifying sensitivity/resolution trade-off in emission imaging system optimization. We propose a task and a figure of merit (FOM) based on 3-class ROC analysis. The task combines detection of a lesion on a variable background with discrimination of a lesion from an adjacent structure, modeled by Rayleigh task. Recently developed practical framework for conducting 3-class ROC analysis is utilized to evaluate the performance of channelized hotelling observer. A primitive imaging system model is used to investigate effects of resolution, sensitivity and imaging time. Volume under ROC surface (VUS) is used as the primary FOM in assessment of the task performance. The FOM is optimal according to several decision strategies. We present results of initial tests of the model properties in a simplified planar imaging setting. We observe that system resolution requirements are critical for observer performance in the proposed task. Initial experience shows that the new approach provides useful insight into factors affecting observer performance in realistic experimental designs.