Luckman et al. (2018) experimentally tested the conjecture that a single model of risky intertemporal choice can account for both risky and intertemporal choices, and under the conditions of their experiment, found evidence supporting it. Given the existing literature, that is a remarkable result which warrants (conceptual) replication. Luckman et al. (2018), following a well-established tradition in psychology, had first-year psychology students participate that were rewarded with non-monetary course credits (see also Luckman et al. 2020), casting shadows of doubt on whether their participants were properly incentivised. Proper incentivization is a long-standing bone of contention among experimentally working economists and psychologists, last but not least when it comes to the elicitation of preferences of any kind. Another reason to be sceptical is that the experiment was not properly powered up; the no-difference results reported by the authors might be spurious. In our conceptual replication, we find significant differences between the risky and intertemporal choices at both the group and individual level. We find further that there is no significant difference between choices made by participants that are paid a flat incentive and participants that are paid under the random incentive scheme, at the group level. We find that order effects matter for intertemporal choices, but not for risky choices. At the individual level, we find evidence in favour of the model that assumes a common value function, but separate choice functions. This result is robust across the incentive systems, and order of presentation, but sensitive to different prior distributions.