Andreoni and Sprenger (2012) proposed the “Convex Time Budgets (CTB)” method to estimate preference parameters that govern individuals’ intertemporal decision making. Their method implements intertemporal budget constraints that involve payments at two different points in time. Individuals are asked to allocate a monetary budget to the two dated payments, with a (nonnegative) constant interest rate being paid for every monetary unit allocated to the later payment. The main promise of this methodology is a precise identification of the preference parameters that describe individuals’ choices. This, however, holds only as long as individuals choose interior solutions. It has turned out that about two-thirds of all choices that subjects make in lab experiments are corner solutions. Since a large share of corner solutions deprives the CTB of its main advantage, we propose a method to substantially decrease the frequency at which subjects choose corner solutions. The main idea is that the interest rate is initially very high and strictly decreases in the amount that subjects allocate to the later payment. Thus, the convex time budgets become strictly convex. The extremely high initial interest rate should discourage individuals from allocating the entire budget to the earlier payment, while the marginal interest rate approaching zero (or even becoming negative) if the entire budget is saved should discourage subjects from allocating the entire budget to the later payment. We conduct a series of experiments and indeed find that strictly convex budgets dramatically decrease the number of corner solutions compared to linear budgets.