Most interactions between Business Angels (BAs) and fund-seeking entrepreneurs end in failure. Research into the causes of this high failure rate has been constrained by the private nature of the BA-entrepreneur interaction. We take advantage of a rich set of videotaped BA-entrepreneur interactions to investigate whether BAs use rational decision-making approaches that consider all relevant information or use heuristics that trade off accuracy for efficiency in order to reject business opportunities early in the investment-decision process. In doing so we pay particular attention to the multiple criteria used by BAs to assess the potential of these opportunities in terms of investment return and investment risk, as well as the reasons used to reject these opportunities. We hypothesize that BAs make trade offs between market potential, product adoption, protectability, and entrepreneur experience to reject opportunities due to insufficient return and that they also trade off between technology risk, operational risk, market risk and financial risk to reject opportunities due to excess investment risk. We also postulate that BAs do not trade off between investment return and investment risk when rejecting an opportunity, rather they reject opportunities that fail to meet an aspiration level for investment return as well as an aspiration level for investment risk.