Intertemporal choices simultaneously activate discounting, risk aversion, and intertemporal substitution. Future risk stimulates, more specially, higher-order aspects of preference. While a vast empirical literature has studied discounting, risk preferences, and basic consumption smoothing, empirical knowledge of higher-order preferences is still scarce. Based on a two-period consumption/saving model, we investigate the interaction of risk and time preferences in intertemporal decisions with future risk. We show that the main carriers of saving variation in intertemporal decisions under risk, according to the model, are intertemporal preferences. Risk preferences only play a minor role. The predictions under Expected Utility (EU) resemble those of the intertemporal-substitution component of recursive utility, not the risk component. Our simulations also show that second- and third-derivative effects are the most essential features of preferences in the decisions in question. Effects already from the fourth order on have essentially no impact. While the risk effects under EU are stronger than under recursive preferences, the few-relevance result regarding third- and higher-order risk effects persists. For a deepened understanding of preferences underlying intertemporal choice, correctly identifying intertemporal preference seems to be the single most critical aspect. The quantitative differences in the predictions for EU and recursive preferences may allow to empirically discriminate between the preference concepts.