Host bird species of the Eurasian Cuckoo, Cuculus canorus, often display egg-discrimination behaviour but chick-rejection behaviour has never been reported. In this paper, we analyse a host-cuckoo association in which both population dynamics and evolutionary dynamics are explored in a discrete-time model. We introduce four host types, each with their own defence behaviour, displaying either egg or chick rejection, neither or both, We also introduce fitness functions for each of these host types. Although we can characterize the long term behaviour in many cases by a simple heuristic argument which is in accordance with common views in ecology, there are a number of other phenomena that are not explained within this framework: we describe stable oscillatory behaviour and coexistence of two defensive host types. We analyse the scenarios in which chick rejection may establish itself and give a first explanation as to why this defence trait has never been recorded in nature. We find that chick rejectors generally are at an intrinsic disadvantage with respect to a host type that rejects eggs. Hosts benefit more from rejecting cuckoo eggs than cuckoo chicks, and our model suggests that this is chiefly responsible for the absence of chick rejection. Moreover, even though it seems that chick rejection must be useful as an extra defence, it is shown that hosts with both defence strategies are less likely to establish themselves in competition with egg-rejectors than hosts which reject chicks only. These results provide insight in the extent to which adaptations may be perfected by natural selection.