Fluorescence in situ hybridization (FISH) is a molecular diagnostic technique in which a fluorescent labeled probe hybridizes to a target nucleotide sequence of deoxyribose nucleic acid. Upon excitation, each chromosome containing the target sequence produces a fluorescent signal (spot). Because fluorescent spot counting is tedious and often subjective, automated digital algorithms to count spots are desirable. New technology provides a stack of images on multiple focal planes throughout a tissue sample. Multiple-focal-plane imaging helps overcome the biases and imprecision inherent in single-focalplane methods. This paper proposes an algorithm for global spot counting in stacked three-dimensional slice FISH images without the necessity of nuclei segmentation. It is designed to work in complex backgrounds, when there are agglomerated nuclei, and in the presence of illumination gradients. It is based on the morphological tophat transform, which locates intensity spikes on irregular backgrounds. After finding signals in the slice images, the algorithm groups these together to form three-dimensional spots. Filters are employed to separate legitimate spots from fluorescent noise. The algorithm is set in a comprehensive toolbox that provides visualization and analytic facilities. It includes simulation software that allows examination of algorithm performance for various image and algorithm parameter settings, including signal size, signal density, and the number of slices.