Large health care data bases afford the exciting opportunity to study effects of treatments and exposures on rare outcomes and adverse events, providing important information for clinicians and policy makers considering novel treatment strategies or health care policies. Even in such large databases, the number of observed outcomes may be small, while the number of putative confounders may be very large in comparison. Standard confounder-adjusted estimators of causal effects often behave erratically in these situations. However, it is often possible to improve on the finite-sample performance of asymptotically efficient estimators of causal effects by considering estimation in a statistical model that enforces bounds on the incidence of the outcome in the population of interest. These bounded estimators have been proposed in several contexts, including estimation of causal effects of single- and multiple-timepoint treatments, as well as estimation of effects on the cumulative incidence of an outcome in the presence of competing risks. In this talk, I will review these recent developments and discuss doubly robust methods that preserve valid inference even when model bounds are misspecified.