Palimpsests and anomalous pit craters are two classes of craters found on the icy satellites Ganymede and Callisto that have no obvious counterparts among the crater populations found on rocky planets. The distinct characteristics of palimpsests and anomalous pit craters in morphology, morphometry, and population statistics, which differentiate them from the numerous ''normal'' craters and basins on the icy satellites, also preclude their origin as normal craters that have nearly vanished through viscous relaxation. An alternate origin is proposed: palimpsests are formed when the flow of material during the modification stage of crater formation is dominated by 'wet' fluid flow as opposed to 'dry' granular flow, which forms normal craters; conditions of 'wet' modification flow occur when the volume of melt remaining in the crater attains a volume comparable to the volume of the transient crater. By use of an impact model that includes: (1) plausible impact velocity distributions, (2) crater scaling in ice. (3) shock melting in ice, (4) thermal profiles as a function of time in Ganymede, and (5) cratering flow field constraints, conditions for wet modification flow are found to occur for sufficiently large impacts or high-velocity impactors. The range of normal crater-palimpsest transition diameters and the morphologic characteristics inferred from the impact model are consistent with the observed characteristics of palimpsests. Thus normal craters are inferred to result from the majority of impactors which have impact velocities near the average of 15 km/s, anomalous pit craters (inferred to be transitional forms) from intermediate velocity impactors at about 30 km/s, and palimpsests by impactors travelling in excess of about 40 km/s. The thermal state of the crust at the time of impact is a second-order effect, but sufficient to account for the difference in palimpsest population between Ganymede and Callisto if Ganymede once had a liquid mantle while Callisto remained unmelted and undifferentiated or solidified prior to the formation of the presently observed crater population.