Can agents rationally inquire into things that they know? On my view, the answer is yes. Call this view the Compatibility Thesis. One challenge to this thesis is to explain why assertions like “I know that p, but I’m wondering whether p” sound odd, if not Moore-Paradoxical. In response to this challenge, I argue that we can reject one or both premises that give rise to it. First, we can deny that inquiry requires interrogative attitudes. Second, we can deny the ignorance norm, on which agents are not permitted to both know and have interrogative attitudes, such as wondering. I argue that there are compelling reasons to deny the former and reasons to question the latter. Both options pave the way for further work on further inquiry.