Leaders from across the political spectrum are often accused of manipulating the media to their benefit. Contemporary developments have proliferated the number of media sources available to citizens. We argue that new, independent media sources may actually be a boon for vulnerable leaders. In a simple formal model, we give citizens a limited capacity for attention and allow states to expend effort to selectively obstruct information sources. We demonstrate a phenomenon of “displacement”—where the presence of alternative sources of information can actually reduce the required effort for states to succeed in obfuscating citizen learning. This is because alternative media sources mean that states only need to divert citizen attention without resorting to complete obstruction, reducing the necessary effort expended. This result advances our understanding of how contemporary states navigate increasingly complex media landscapes. We supplement the model with discussions of the media policies of Malaysian and Turkish governments.