This paper investigates the shape of the utility function for losses. From a rational point of view it can be argued that utility should be concave. Empirically, measurements of the utility for losses show mixed results but most evidence supports convex rather than concave utilities. However, these measurements use methods that are either biased by the certainty effect or require complex parametrical estimations. This paper re-examines utility for losses, avoiding the mentioned pitfalls by using the tradeoff method. We find that utility for losses is convex. This is contrary to common assumption in the economics literature. Also, we investigate properties of the tradeoff method showing a new violation of procedure invariance. Our findings demonstrate that diminishing sensitivity is an important phenomenon for utility elicitation.