Context. This work is a follow-up of a previous study, where we simulated the dynamical evolution of the Oort Cloud over 5 Gyr with special attention to the injection of comets into observable orbits. Aims. We wish to clarify how comet injection operates with two types of perturbers: Galactic tides and passing stars. We illustrate why attempts to identify the stars that might have played an important role in injecting the observed new Oort Cloud comets are as yet unlikely to succeed, and investigate how large an improvement can be expected from the Gaia mission. Methods. We simulate a 5 Gyr time span, concentrating on the injections found during the last 3 Gyr by extracting detailed information about the last revolution of the injected comets. We analyse the contributions of both the Galactic tides and the stars separately, and assess their importance as a function of the semi-major axis of the comets. We also compute the distances and motions of the perturbing stars at the time the comets reach their perihelia and thus estimate their observability. Results. By studying more than 20 000 injected comets, we determine how the likelihood of tidal and stellar injections varies with the semi-major axis. We establish the range of semi-major axis for which a real-time synergy between stellar and tidal perturbations is important. We find how many perturbing stars could be identified using HIPPARCOS and Gaia data, and how the dynamics of injections would change, if only the observable stars were acting. Conclusions. The number of injected comets peaks at a semi-major axis (a) of about 33 000 AU but the comets spread over a wide range around this value. The tides are unable to inject any comets at a < 23 000 AU but would be able to inject almost all of them at a > 50 000 AU. The real-time synergy is found to extend between a similar to 15 000 AU and a similar to 45 000 AU and to be the main contributor at a similar to 25 000 AU. Stellar perturbations make important contributions at all semi-major axes. On the basis of HIPPARCOS data, only a minority of the stars that may contribute to comet injections are detectable, since most stars have escaped to distances beyond the HIPPARCOS detection limit. For Gaia, on the other hand, a large majority of the perturbing stars will be both identifiable and measurable.