Touchpad devices are widely used but lacking in pointing efficiency. The TouchGrid, an instance of what we term cell cursors, replaces moving the cursor through dragging the finger on a touchpad with tapping in different regions of the touchpad. The touchpad regions are recursively mapped to smaller display regions and thereby enable high-precision pointing without requiring high tapping precision. In an experiment, six subjects used the TouchGrid and a standard touchpad across different numbers of targets, distances to targets, and target widths. Whereas standard touchpad operation follows Fitts' law, target selection time with the TouchGrid is a linear function of the required number of taps. The TouchGrid was significantly faster for small targets and for tasks requiring one tap, and marginally faster for two-tap tasks. Error rates tended to be higher with the TouchGrid than the standard touchpad. All subjects preferred the TouchGrid.