In grasping studies, maximum grip aperture (MGA) is commonly used as an indicator of the object size representation within the visuomotor system. However, a number of additional factors, such as movement safety, comfort, and efficiency, might affect the scaling of MGA with object size and potentially mask perceptual effects on actions. While unimanual grasping has been investigated for a wide range of object sizes, so far very small objects (<5 mm) have not been included. Investigating grasping of these tiny objects is particularly interesting because it allows us to evaluate the three most prominent explanatory accounts of grasping (the perception-action model, the digits-in-space hypothesis, and the biomechanical account) by comparing the predictions that they make for these small objects. In the first experiment, participants ( ) grasped and manually estimated the height of square cuboids with heights from 0.5 to 5 mm. In the second experiment, a different sample of participants ( ) performed the same tasks with square cuboids with heights from 5 to 20 mm. We determined MGAs, manual estimation apertures (MEA), and the corresponding just-noticeable differences (JND). In both experiments, MEAs scaled with object height and adhered to Weber's law. MGAs for grasping scaled with object height in the second experiment but not consistently in the first experiment. JNDs for grasping never scaled with object height. We argue that the digits-in-space hypothesis provides the most plausible account of the data. Furthermore, the findings highlight that the reliability of MGA as an indicator of object size is strongly task-dependent.