Disease control can induce both demographic and evolutionary responses in host-parasite systems. Foreseeing the outcome of control therefore requires knowledge of the eco-evolutionary feedback between control and system. Previous work has assumed that control strategies have a homogeneous effect on the parasite population. However, this is not true when control targets those traits that confer to the parasite heterogeneous levels of resistance, which can additionally be related to other key parasite traits through evolutionary trade-offs. In this work, we develop aminimal model coupling epidemiological and evolutionary dynamics to explore possible trait-dependent effects of control strategies. In particular, we consider a parasite expressing continuous levels of a trait-determining resource exploitation and a control treatment that can be either positively or negatively correlated with that trait.We demonstrate the potential of trait-dependent control by consideringthat the decision maker may want to minimize both the damage caused by the disease and the use of treatment, due to possible environmental or economic costs. We identify efficient strategies showing that the optimal type of treatment depends on the amount applied. Our results pave the way for the study of control strategies based on evolutionary constraints, such as collateral sensitivity and resistance costs, which are receiving increasing attention for both public health and agricultural purposes