The mass use of an effective vaccine clearly has the potential to provide major health benefits in terms of a reduction in the total number of infected cases, and therefore a reduction in the total number of adverse effects [1, 3, 7] . However, when used against an ongoing epidemic, the logistical constraints in terms of the speed with which vaccine can be manufactured and administered means that its deployment must be carefully targeted [8, [11] [12] [13] [14] [15] 23, 26, 27] . Many of these have focused on particular aspects of targeted vaccination (such as age-or risk-based) or have developed approximate [26] or analytical [27] methods for optimal targeting. Here, using standard differential equation models augmented to reflect particular heterogeneities, we have attempted to provide a relatively general framework that will be familiar with public-health epidemiologists and other non-specialist modellers. In general, our results agree with those of earlier studies although we have often attempted to consider a farwider parameter space, with the aim of spanning much of the parameter uncertainty that is likely to arise during the early stages of an epidemic.