tokens: resonant stripes, where comets have experienced secular eccentricity pumping. This sometimes goes in the direction of circularizing the orbits, but very often leads into the sungrazing end state. This structure would be smeared out in the plot by Levison et al. ( 2006 ; their Fig. 1b) but, most likely, in reality it does not exist. The small nudges given to the comets in their integrations would inhibit the long-term action of these resonances in most cases (see Valsecchi et al. 1995 ), while we introduced the artefact of leaving the comets entirely in the hands of the giant planets. We find that deflected comets get dynamically ejected only if their starting semi-major axis is larger than 2.6 au. For smaller values, if Jupiter-crossing occurs, it is only for very high eccentricity, so encounters are rare and inefficient in changing the orbits. In these cases, collision with the Sun is very likely, and many of the survivors are “saved by the bell”, since our integrations stop after 100 000 revolutions. Looking at the statistics of end states for the deflected comets, we find a remarkably high probability (more than 12%) of collision with the Sun, and most of these belong to the above-mentioned category. We derived the steady-state number of comets in the Encke-like domain and made a comparison with the results of Levison et al. (2006) , which are quite different. In fact, using our first approximation to the transfer mechanism, we predict only of the number of Encke-like comets found by Levison et al. (2006) . Thus, our method is severely lacking in transfer efficiency, and several reasons for this are easily identifiable. First, consider the limitation caused by cutting the integrations to a total of 100 000 revolutions. Compare this to the example provided by Levison et al. (2006) of a comet meeting their requirement for an Encke-like comet. Before this happens, the comet spends a million years (roughly 250 000 orbits) in a decoupled state waiting for the completion of its transfer. If this situation is typical, we missed most of the transfers by stopping the integrations too early. Moreover, as in the case mentioned, most transfers may require several interventions by terrestrial planets – something that our procedure forbids. It is true that more than one encounter as close as those that we modelled is not likely to occur for the same object. However, significant perturbations may be caused by the more distant and more frequent encounters that our procedure neglects. The main reason for the inefficiency of our transfer model appears to be the premature cutting of the integrations and the limitation to the closest encounters, which are too rare to have a large effect. If we had integrated all the comets until ejection or collision, some more deflections would have occurred. However, the increase would not be large, as seen from the fact that more than 80% of the deflections that we followed up by further integrations happened before the 50
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