The understanding of trade-offs between behaviours is fundamental to the study of animal behaviour. Individuals may often be faced with the choice of which of two mutually incompatible behaviours to perform. Here, I present a model investigating the trade-off between two behaviours, where one of the behaviours is crucial to the success of the other. I illustrate the results with examples, considering particularly a trade-off between territorial defence and courtship. I investigate how the ability of an individual to perform the behaviours changes the time or energy allocated to each behaviour. Intuition suggests that the time invested in performing a behaviour should decline as the individual's ability to perform the behaviour increases. Explicit, quantitative modelling suggests that this is not always the case. Instead, we see a pattern where investment in one of the behaviours at first increases and then decreases as the ability to perform the behaviour increases. This finding has implications for the empirical study of trade-offs between behaviours, since it could appear that individual ability has no effect on the trade-off under consideration. I discuss potential methods for distinguishing whether time allocation changes in a counter-intuitive, non-monotonic way with increasing individual ability, or whether there is indeed no effect.