The law establishing Obamacare was officially titled the Patient Protection and Affordable Care Act. And the “affordable” bit wasn’t just about subsidizing premiums. It was also supposed to be about “bending the curve” — slowing the seemingly inexorable rise in health costs.

Much of the Beltway establishment scoffed at the promise of cost savings. The prevalent attitude in Washington is that reform isn’t real unless the little people suffer; serious savings are supposed to come from things like raising the Medicare age (which the Congressional Budget Office recently concluded would, in fact, hardly save any money) and throwing millions of Americans off Medicaid. True, a 2011 letter signed by hundreds of health and labor economists pointed out that “the Affordable Care Act contains essentially every cost-containment provision policy analysts have considered effective in reducing the rate of medical spending.” But such expert views were largely ignored.

So, how’s it going? The health exchanges are off to a famously rocky start, but many, though by no means all, of the cost-control measures have already kicked in. Has the curve been bent?The answer, amazingly, is yes. In fact, the slowdown in health costs has been dramatic.

O.K., the obligatory caveats. First of all, we don’t know how long the good news will last. Health costs in the United States slowed dramatically in the 1990s (although not this dramatically), probably thanks to the rise of health maintenance organizations, but cost growth picked up again after 2000. Second, we don’t know for sure how much of the good news is because of the Affordable Care Act.

Still, the facts are striking. Since 2010, when the act was passed, real health spending per capita — that is, total spending adjusted for overall inflation and population growth — has risen less than a third as rapidly as its long-term average. Real spending per Medicare recipient hasn’t risen at all; real spending per Medicaid beneficiary has actually fallen slightly.

What could account for this good news? One obvious answer is the still-depressed economy, which might be causing people to forgo expensive medical care. But this explanation turns out to be problematic in multiple ways. For one thing, the economy had stabilized by 2010, even if the recovery was fairly weak, yet health costs continued to slow. For another, it’s hard to see why a weak economy would have more effect in reducing the prices of health services than it has on overall inflation. Finally, Medicare spending shouldn’t be affected by the weak economy, yet it has slowed even more dramatically than private spending.

A better story focuses on what appears to be a decline in some kinds of medical innovation — in particular, an absence of expensive new blockbuster drugs, even as existing drugs go off-patent and can be replaced with cheaper generic brands. This is a real phenomenon; it is, in fact, the main reason the Medicare drug program has ended up costing less than originally projected. But since drugs are only about 10 percent of health spending, it can only explain so much.

So what aspects of Obamacare might be causing health costs to slow? One clear answer is the act’s reduction in Medicare “overpayments” — mainly a reduction in the subsidies to private insurers offering Medicare Advantage Plans, but also cuts in some provider payments. A less certain but likely source of savings involves changes in the way Medicare pays for services. The program now penalizes hospitals if many of their patients end up being readmitted soon after being released — an indicator of poor care — and readmission rates have, in fact, fallen substantially. Medicare is also encouraging a shift from fee-for-service, in which doctors and hospitals get paid by the procedure, to “accountable care,” in which health organizations get rewarded for overall success in improving care while controlling costs.

Furthermore, there’s evidence that Medicare savings “spill over” to the rest of the health care system — that when Medicare manages to slow cost growth, private insurance gets cheaper, too.

And the biggest savings may be yet to come. The Independent Payment Advisory Board, a panel with the power to impose cost-saving measures (subject to Congressional overrides) if Medicare spending grows above target, hasn’t yet been established, in part because of the near-certainty that any appointments to the board would be filibustered by Republicans yelling about “death panels.” Now that the filibuster has been reformed, the board can come into being.

The news on health costs is, in short, remarkably good. You won’t hear much about this good news until and unless the Obamacare website gets fixed. But under the surface, health reform is starting to look like a bigger success than even its most ardent advocates expected.