Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of upper and lower bounds on the potential outcomes of decision alternatives to assess risks and benefits.We show that, in such cases, we can improve sample efficiency by estimating simple functions that bound these outcomes instead of estimating theirconditional expectations, which may be complex and hard to estimate. Our analysis highlights a trade-off between the complexity of the learningtask and the confidence with which the learned bounds hold. Guided by these findings, we develop an algorithm for learning upper and lowerbounds on potential outcomes which optimize an objective function defined by the decision maker, subject to the probability that bounds are violatedbeing small. Using a clinical dataset and a wellknown causality benchmark, we demonstrate that our algorithm outperforms baselines, providing tighter, more reliable bounds.