We introduce Intelligent Annotation Dialogs for bounding box annotation. We train an agent to automatically choose a sequence of actions for a human annotator to produce a bounding box in a minimal amount of time. Specifically, we consider two actions: box verification [34], where the annotator verifies a box generated by an object detector, and manual box drawing. We explore two kinds of agents, one based on predicting the probability that a box will be positively verified, and the other based on reinforcement learning. We demonstrate that (1) our agents are able to learn efficient annotation strategies in several scenarios, automatically adapting to the image difficulty, the desired quality of the boxes, and the detector strength; (2) in all scenarios the resulting annotation dialogs speed up annotation compared to manual box drawing alone and box verification alone, while also outperforming any fixed combination of verification and drawing in most scenarios; (3) in a realistic scenario where the detector is iteratively re-trained, our agents evolve a series of strategies that reflect the shifting trade-off between verification and drawing as the detector grows stronger.