“Advantageous selection” occurs when an increase in the insurance premium induces insured individuals with high costs to quit, thereby reducing the average cost among remaining buyers. Many have motivated the existence of advantageous selection by differences in risk aversion between individuals, implying varying insured risk avoidance efforts. We argue that it may also appear under different circumstances. We show A) that firm profit maximization implies that advantageous selection is more likely when markup rates and the price sensitivity of insurance demand are high; and B) that it may occur when several contracts are offered, when individuals also face a non-insurable background risk, or when they face two mutually exclusive risks bundled together in a single insurance policy. We use Canadian survey data to explore an example of the latter: life care annuities, which bundle long-term care insurance and annuities.