The sputtering yield induced by keV hydrogen ions measured at CERN and at Risø National Laboratory for solid H2 and D2 at temperatures below 4.2 K decreases with increasing film thickness from about 100 x 10(15)molecules/cm2. For a film thickness comparable to or larger than the ion range the data from Risø show a slight increase, whereas the yield from CERN continues to decrease up to very large film thicknesses, i.e. one order of magnitude larger than the ion range. The different behavior of the yield is discussed in terms of the probable growth modes of the films. The films produced at the Risø setup are quench-condensed films, while those produced at CERN are supposed to grow with large hydrogen aggregates on top of a thin bottom layer.