The exploration/exploitation trade-off (EE trade-off) describes how, when faced with several competing alternatives, decision-makers must often choose between a known good alternative (exploitation) and one or more unknown but potentially more rewarding alternatives (exploration). Prevailing theory on how humans perform the EE trade-off states that uncertainty is a major motivator for exploration: the more uncertain the environment, the more exploration that will occur. The current article examines whether exploratory behavior in both choice and attention may be impacted differently depending on whether uncertainty is onset suddenly (unexpected uncertainty), or more slowly (expected uncertainty). It is shown that when uncertainty was expected, participants tended to explore less with their choices, but not their attention, than when it was unexpected. Crucially, the impact of this "protection from uncertainty" on exploration only occurred when participants had an opportunity to learn the structure of the task before experiencing uncertainty. This suggests that the interaction between uncertainty and exploration is more nuanced than simply more uncertainty leading to more exploration, and that attention and choice behavior may index separate aspects of the EE trade-off.