Crop insurance contracts typically constrain the choice of price at which indemnification occurs to be less than the expected output price. This restriction is first analyzed assuming only risk averse farmers, and yield and price uncertainty. General conditions under which the optimal price selection is bounded above by the expected output price are found to be difficult to derive. The results of numerical simulations based on a range of different utility functional forms are presented, and a strong tendency is observed for the optimal price selection to be bounded from below by the expected output price. The effect of increasing output price variability on the optimal price selection is also considered. The simulation results suggest that the optimal price selection is often non-increasing with a mean-preserving spread of the output price distribution. Lastly, it is noted that even in the presence of hidden-action moral hazard, if the incentives for shirking are not too high, then constraint that price selections be lower than the expected output price may still be binding.