This work describes a systematic evaluation of several autofocus functions used for analytical fluorescent image cytometry studies of counterstained nuclei. Focusing is the first step in the automatic fluorescence in situ hybridization analysis of cells. Thirteen functions have been evaluated using qualitative and quantitative procedures. For the last of these procedures a figure-of-merit (FOM) is defined and proposed. This new FOM takes into account five important features of the focusing function. Our results show that functions based on correlation measures have the best performance for this type of image.