Currently available health insurance contracts often fail to insure long-term illnesses: sick people can suffer large increases in premiums or denial of coverage. I describe insurance contracts that solve this problem. Their key feature is a severance payment. A person who is diagnosed with a long-term illness and whose premiums are increased receives a lump sum equal to the increased present value of premiums. This lump sum allows him or her to pay the higher premiums required by any insurer. People are not tied to a particular insurer or a group, and the improvement is free: insurance companies can operate at zero economic profits, and consumers can pay exactly the same premium they do with standard contracts.