We consider inference based on linear conditional moment inequalities, which arise in a wide variety of economic applications, including many structural models. We show that linear conditional structure greatly simplifies confidence set construction, allowing for computationally tractable projection inference in settings with nuisance parameters. Next, we derive least favorable critical values that avoid conservativeness due to projection. Finally, we introduce a conditional inference approach which ensures a strong form of insensitivity to slack moments, as well as a hybrid technique which combines the least favorable and conditional methods. Our conditional and hybrid approaches are new even in settings without nuisance parameters. We find good performance in simulations based on Wollmann (2018), especially for the hybrid approach.