A new scheme for simulating meteor showers is introduced, based on a hybridization of current numerical modelling techniques. It involves an iterative method that generates particles which hit a real-scale Earth, removing the spatial and temporal blurring common to other modelling techniques. The scheme is applied to the activity profile of the Leonids 2001 using three different models of meteoroid ejection velocity and then applied to the Leonids 1998–2000 using the most favourable models. It is shown that to reproduce the observed meteor activity profiles there must be a strong concentration of ejection around perihelion. The modelling also implies that meteoroid density must be towards the higher end of the currently acceptable range, although the derived limits are not independent of the ejection velocity model. We also find that the extreme narrowness of Leonid activity peaks is not easily reproduced with outgassing over the entire day side of the comet but it is fitted well by outgassing in a restricted direction as one would expect from an outgassing jet. In addition, we show that double-peaked features, corresponding to a semihollow meteoroid streamlet, can arise in a meteor shower activity profile from outgassing during a single perihelion passage of the parent comet. It is suggested that this process caused the double-peaked feature in the first maxima of the 2001 Leonids.