We propose a novel experimental method to elicit preference parameters: choices subject to strictly concave budget restrictions. We aim to improve upon the informational content of commonly used methods such as choices subject to linear budget restrictions in two ways: (i) by reducing the number of corner allocations and (ii) by enlarging the range of estimable parameter values. An online study on risk and time preferences confirms the benefits of our method. Corner allocations are drastically reduced, which facilitates estimation on the individual level, and a richer distribution of preference parameters compared to using linear budget restrictions is elicited.