An attempt of finding an appropriate number of convolutional layers in convolutional neural networks is made. The benchmark datasets are CIFAR-10, NORB and EEACL26, whose diversity and heterogeneousness must serve for a general applicability of a rule presumed to yield that number. The rule is drawn from the best performances of convolutional neural networks built with 2 to 12 convolutional layers. It is not an exact best number of convolutional layers but the result of a short process of trying a few versions of such numbers. For small images (like those in CIFAR-10), the initial number is 4. For datasets that have a few tens of image categories and more, initially setting five to eight convolutional layers is recommended depending on the complexity of the dataset. The fuzziness in the rule is not removable because of the required diversity and heterogeneousness.