We discuss a government’s incentives to delegate regulation to bureaucrats. The government faces a trade-off in its delegation decision: bureaucrats have knowledge of the firms in the industry that the government does not have, but at the same time, they have other preferences than the government, so-called bureaucratic drift. We study how the bureaucratic drift and the firm's private information interact to affect the incentives to delegate regulation. Furthermore, we discuss how constrained delegation, i.e., delegation followed by laws and regulations that restrict bureaucratic discretion, increases the scope of delegation. We characterize the optimal delegation rule and show that, in equilibrium, three different regimes can arise that differ in the extent of bureaucratic discretion: no delegation, strict delegation, and weak delegation. We find that bureaucratic discretion reduces with bureaucratic drift. Because of the nature of the regulation problem, the effect of increased uncertainty about the firm's technology on the bureaucratic discretion depends on how that uncertainty changes.