In health insurance, a traditional deductible (i.e. with a deductible range [0,d]) is in theory not effective in reducing moral hazard for individuals who know (ex-ante) that their expenditures will exceed the deductible amount d, e.g. those with a chronic disease. To increase the effectiveness, this paper proposes to shift the deductible range to [s(i),s(i)+d], with starting point s(i) depending on relevant risk characteristics of individual i. In an empirical illustration we assume the optimal shift to be such that the variance in out-of-pocket expenditures is maximized. Results indicate that for the 10-percent highest risks in our data the optimal starting point of a euro1000-deductible is to be found (far) beyond euro1200, which corresponds with a deductible range of [1200,2200] or further. We conclude that, compared to traditional deductibles, shifted deductibles with a risk-adjusted starting point lower out-of-pocket expenditures and may further reduce moral hazard.