Unemployment insurance (UI) programs traditionally take the form of a single insurance contract offered to job seekers. In this work, we show that offering a menu of contracts can be welfare improving in the presence of adverse selection and moral hazard. When insurance contracts are composed of (i) a UI payment and (ii) a severance payment paid at the onset of unemployment, offering contracts with different ratios of UI benefits to severance payment is optimal under the equivalent of a single-crossing condition: job seekers in higher need of unemployment insurance should be less prone to moral hazard. In that setting, a menu allows the planner to attract job seekers with a high need for insurance in a contract with generous UI benefits, and to attract job seekers most prone to moral hazard in a separate contract with a large severance payment but little unemployment insurance. We propose a simple sufficient statistics approach to test the single-crossing condition in the data.