The optimum detector spatial resolution has been determined for a scintigraphic decision task in which the observer must discriminate between two different distributions of radioactivity in tumours. The two kinds of tumour used are: (i) a solid sphere of increased uptake relative to background, and (ii) a thin spherical shell with high uptake in the shell and no radioactivity within the shell. Both tumours are embedded at the same depth within a cylinder of tissue-equivalent material containing a uniform distribution of radioactivity. On the basis of statistical decision theory, the optimum detector spatial resolution for discriminating between the two tumour activity distributions is predicted. The result of an observer performance experiment substantially agreed with the theoretical prediction, though some discrepancy was found, apparently due to a decrease in observer efficiency at poorer spatial resolution. The experimental result suggests that the optimum FWHM of detector spatial response for the discrimination task considered is about 65% of the tumour radius.