A method for calculating the resultant probability distributions of orbital elements for a small body (a comet, asteroid or meteoroid) after a gravitational encounter with a planet is described. This technique incorporates the frequency of such encounters so that the chance of attaining a certain new orbit per unit time is derived. The use of this technique is then illustrated by considering the effect of Jupiter upon the orbits of near-parabolic comets with perihelia near that planet (q = 5.2 AU) and in the inner solar system (q = 1.0 AU), with prograde (i = 10°) and retrograde (i = 170°) paths. As indicated by previous authors the prograde comets are more easily captured into short-period (P< 20 yr) and intermediate-period (20<P<200 yr) orbits; however, in contradiction to most previous work but in agreement with the results of Stagg and Bailey (submitted to Mon. Not. R. Astron. Soc.) it is found that the comets with smaller perihelia, rather than those with perihelia near Jupiter, have higher capture probabilities. This is apparently due to the fact that a small deflection only is needed to sufficiently decelerate a comet onto a smaller orbit if it makes a near-perpendicular crossing of Jupiter’s path, whereas a larger deflection (to achieve a large orbital change) is needed if the paths are near-parallel. With comparatively modest amounts of computer time this method may be used to calculate the relative capture probabilities as a function of i and q for all values of interest, and is thus a useful precursor to integrations following orbital evolution, since it indicates the most likely avenues whereby shorter-period comets are derived from the near-parabolic flux.