Spots are image details resulting from objects, the projections of which are so small that the inner structure of these objects cannot be resolved from their image. Spot detectors are image operators aiming at the detection and localisation of spots in the image. Most spot detectors can be tuned with parameters. This paper addresses the problem of how to select the parameters. We propose to use carefully designed test images, a performance measure, and numerical optimisation techniques to solve this problem. Several optimisation methods are compared, and their adequacy for spot detector design is tested.