Bringing Down Health Care Costs

In terms of U.S. domestic politics, health care seems to be trumping trade policy these days.  I'd rather talk about trade policy than health care, so I'm going to try to sneak trade policy into the health care discussion by proposing the following:  If we want to bring down health care costs, as just about everybody does, wouldn't it be a good idea to allow more foreign competition in the health insurance industry?