The impact crater distribution observed on the moons of Jupiter and Saturn is more symmetric than that expected from cometary bombardment, which should preferentially scar the leading hemisphere of a synchronously rotating moon. The possibility that cometary impacts may have ''spun up'' these satellites, resulting in an interchange of leading and trailing hemispheres, is investigated. It is found that such a ''spinup'' is unlikely for the Galilean satellites of Jupiter and for Saturn's inner midsized moons.