We describe the design of and first results from a cam-driven portable absolute gravimeter. The cam-based design of a dropper allows us to build a compact system that uses 20 mm of free fall for the measurement. The instrument drops a test mass 200 times a minute (a measurement rate of more than 3 times per second). The centre of mass of the apparatus is kept fixed during the entire measurement cycle, thus avoiding "recoil" effects that could systematically bias the measurement. Seismic isolation is provided by a passive eddy-current-damped simple spring. Measurement results taken at Table Mountain Gravity Observatory (TMGO, Boulder, Colorado), though reproducible at a level of several microgals (1 muGal = 10-8 m/s(2)), show a sensitivity to the measurement start and stop points at the 20 muGal level.