Most Americans agree our health-insurance system is too expensive and leaves too many people uncovered. There isn't much agreement on what to do about it.

President Bush's new proposal doesn't, on first look, seem promising.

That's partly because so many details are yet to be unveiled.

But more important, the proposal launched over the last few days relies on the free market to fix things, without getting at the flaws that make the health-care market so inefficient - such as consumers' virtual inability to shop for care on the basis of price.

The gist of the president's proposal is this: Families that have health insurance would get a new federal tax deduction of $15,000, while single people would get one of $7,500.

At the same time, health insurance received through work would be considered taxable income, based on the cost of the policy.

A family with a deluxe, company-funded health plan costing more than $15,000 would lose out, since the tax on the benefit would be bigger than the tax cut for the $15,000 deduction.

A family with a policy costing less than $15,000 would win because the tax cut from the deduction would be bigger than the tax on the benefit.

The idea is to push people who don't have health coverage at work to buy it on the open market, thus becoming eligible for the deduction, which would offset the policy's cost.

If you were in the 15 percent tax bracket, you could save $2,250 with the deduction (0.15 x $15,000) - but only if you got health insurance.

How far would $2,250 go?

Yesterday, I went to www.ehealthinsurance. com to compare policies for a family of four. The cheapest was $3,360 a year for a policy with a $12,000 out-of-pocket limit. That means the family could pay as much as $12,000 in any given year despite having the insurance. Most office visits and medications were not covered.

At the other end of the scale was a policy covering just about everything for $15,864 a year. Maximum annual out-of-pocket expense was $4,000.

The bulk of the policies cost $6,000 to $7,000 a year with out-of-pocket limits in excess of $8,000.

Would a $2,250 tax cut be enough to get a family of modest means to buy a $6,000 policy? Certainly, some fence-sitters would. But it's anyone's guess how many of those there are.

Also, many of the people who don't have health benefits at work make so little that they are paying tax at less than a 15 percent rate. If your tax rate is, say, 10 percent, the $15,000 deduction would cut your taxes only $1,500. And millions of uninsured Americans pay tax at less than a 10 percent rate.

Nudging more people to shop outside the workplace for health insurance could, in theory, boost competition among insurers, pushing down prices. But the price of health insurance can drop only so far because the cost of health care is so high.

The president's proposal doesn't appear to do anything to address this.

Granted, this is a tough problem. I've long thought the market could benefit if consumers could shop for doctors, hospitals and other providers on the basis of price. Just ask your doctor for a complete price list. She'll look at you in astonishment.

Medical providers should be required to post their prices, in the office and online, so you could search for the best health-care deal, the way you search for the best deal on a new computer or flight to Las Vegas.

To make this effective, consumers would have to benefit from choosing low-cost care. Right now, consumers don't care about price so long as the insurer will cover it.

I imagine the insurers would provide the incentive, offering rebates, frequent-flier miles . . . some reward to policyholders who shunned the most expensive providers.

Maybe there's more to the Bush proposal than it first appears - I'd love to think there will be a real effort to tackle health-care problems.

For now, though, I'm with others who worry that middle-class workers with enviable plans would suffer a tax increase, all in the name of changes that won't do much for people who really need help.