We will start with a brief review of quantum reference frames, which have enjoyed a large amount of attention in recent years. Then we will discuss a current project investigating reference frames whose size, and therefore accuracy, are bounded in some way. This necessarily limits one's ability to prepare states and to perform quantum operations and measurements on a system. As observed on several occasions, the nature of these limitations is similar in many ways to that of decoherence. We investigate how a quantum reference frame of bounded size can be ''dequantized'', i.e., treated as external to the quantum formalism, in such as way as to induce an effective decoherence on any system described with respect to that frame.