Coincidence counting and focusing collimators with different isotopes are compared for detection of brain tumours with external scanning. A modification of Dewey and Sinclair's (1961) figure of merit for the best compromise between resolution and sensitivity for detection of the tumour is measured experimentally using spherical glass bulbs in a tank of water, to represent tumours in the head. The probabilities of detecting tumours of different sizes are calculated for different isotopes making certain assumptions. It is concluded that74As or72As with focusing collimators are better than the other isotopes investigated for detection of brain tumours.125I is not suitable.