During his State of the Union speech, President Obama proposed “ask(ing) more from the wealthiest seniors” as a possible way to save money on Medicare. This isn’t the first time he’s embraced the concept known as means-testing, and it’s an idea I myself floated as one possible compromise between Republicans and Democrats. But it’s also worth keeping in mind that Medicare is already heavily means-tested and it’s unclear how much more room there is for more means-testing.

Just check out this official website outlining the premiums for Medicare recipients. Premiums for Medicare Part B (which covers services like lab tests, surgeries and doctors’ visits) range from $99.90 to $319.60 per month and prescription drug coverage costs wealthier beneficiaries $66.40 more per month than it does for those who receive the standard benefit.

Also, as the recently retired chief actuary of Medicare, Richard Foster, once told me, it’s much more difficult to figure out how to vary deductibles and co-payments by income level. “In practice, administering an income-related benefit package where your deductible might change, or your cost-sharing might change, depending on your income level — that gets to be pretty messy,” Foster said. “Because all that happens at the local doctor’s office, or at the hospital. And then you have to know not just what insurance coverage you have, but what income category you fall into, and that’s not straightforward. Policymakers could if they wanted to change the basis for income-related premiums.”

So, though there may be some savings to be had by further means-testing of premiums, given that the program is already heavily means-tested, the savings would be nowhere near what’s needed to make the program sustainable over the long haul.