The U.S. Supreme Court Thursday struck down part of Minnesota law that forces people suspected of driving under the influence to submit to blood tests without a warrant or risk potentially more severe penalties.

At the same time, however, the high court affirmed a Minnesota Supreme Court ruling that authorities can force a person to submit to breath tests without a warrant by criminalizing their refusal to do so.

The court ruled in three consolidated cases, one of which involved William Bernard, who was stopped by police in South St. Paul after they received a tip that three drunk men had jumped in a pickup truck at the public boat launch on the Mississippi River.

By the time they got there, Bernard was walking dazed in his underwear, his pickup truck hung up on the edge of the boat ramp. All smelled of alcohol.

Bernard, who had four previous convictions for DUI, admitted to drinking, but said he wasn’t driving the truck, and he refused to take a chemical test.

In upholding the validity of the breath test without a warrant in February 2015, Minnesota Supreme Court chief Justice Lorie Gildea said “the breath test was a search of Bernard’s person that would have been no more intrusive than the myriad of other searches of the body that we and other courts have upheld as searches incident to a valid arrest.”

Today, the U.S. Supreme Court said essentially the same thing.

“Because the impact of breath tests on privacy is slight, and the need for BAC testing is great, the Fourth Amendment permits warrantless breath tests incident to arrests for drunk driving. Blood tests, however, are significantly more intrusive, and their reasonableness must be judged in light of the availability of the less invasive alternative of a breath test. Respondents have offered no satisfactory justification for demanding the more intrusive alternative without a warrant. In instances where blood tests might be preferable — e.g., where substances other than alcohol impair the driver’s ability to operate a car safely, or where the subject is unconscious — nothing prevents the police from seeking a warrant or from relying on the exigent circumstances exception if it applies. Because breath tests are significantly less intrusive than blood tests and in must cases amply serve law enforcement interests, a breath test, but not a blood test, may be administered as a search incident to a lawful arrest for drunk driving. No warrant is needed in this situation.

Five Supreme Court justices said motorists cannot be criminally punished for refusing to submit to a blood test, however. It ruled in a case involving a North Dakota man who refused to allow blood to be drawn.

“It is one thing to approve implied-consent laws that impose civil penalties and evidentiary consequences on motorists who refuse to comply, but quite another for a State to insist upon an intrusive blood test and then to impose criminal penalties on refusal to submit. There must be a limit to the consequences to which motorists may be deemed to have consented by virtue of a decision to drive on public roads.

Refusing to submit to breath testing in Minnesota carries consequences often more severe than a DUI conviction, particularly in cases with previous DUI convictions. In Minnesota, 1 in 7 drivers has such a conviction.

And that, Justice Samuel Alito wrote in his opinion (joined by Justices Stephen Breyer, Anthony Kennedy, Elena Kagan and John Roberts) is the way it needs to be.

“If the penalty for driving with a greatly elevated BAC or for repeat violations exceeds the penalty for refusing to submit to testing, motorists who fear conviction for the more severely punished offenses have an incentive to reject testing. And in some States, the refusal rate is high.

On average, over one-fifth of all drivers asked to submit to BAC testing in 2011 refused to do so,” he said.

Alito said Minnesota’s law is why the state’s refusal rate is half the 24% rate reported for 1988, the year before its first criminal refusal law took effect.

Bernard’s attorney argued, however, that even the breath test is intrusive and should require a warrant.

Alito was unmoved, saying the test is neither painful nor difficult, sucking on a straw more than four times.

“The use of a straw to drink beverages is a common practice and one to which few object,” he wrote.

Besides, he maintained, air isn’t part of our bodies and the test only reveals one thing: how much alcohol is in a person’s breath.

“Humans have never been known to assert a possessory interest in or any emotional attachment to any of the air in their lungs,” he said. “The air that humans exhale is not part of their bodies. Exhalation is a natural process—indeed, one that is necessary for life. Humans cannot hold their breath for more than a few minutes, and all the air that is breathed into a breath analyzing machine, including deep lung air, sooner or later would be exhaled even without the test.”

But blood tests are a different matter entirely.

“It is significantly more intrusive than blowing into a tube,” Alito wrote. “Perhaps that is why many States’ implied consent laws, including Minnesota’s, specifically prescribe that breath tests be administered in the usual drunk-driving case instead of blood tests or give motorists a measure of choice over which test to take.”

The court overturned the conviction of a North Dakota man for refusing to submit to a blood test, declaring it an unreasonable search.

Why the rush to draw blood without a warrant? Authorities say in the time it takes to get one, it’s possible alcohol in a person can dissipate.

In her dissent, Justice Sonia Sotomayor focused on the South St. Paul case.

She said most breath tests in Minnesota are not performed roadside, but usually 45 minutes after a person is detained, long enough, for example, for a driver to contact an attorney. That’s plenty of time to also get a warrant, she argued.

While Alito argued doing so would overburden judges, Sotomayor’s math showed that on average, judges would be required to issue one more warrant a week in Minnesota.

“This Court has never said that mere convenience in gathering evidence justifies an exception to the warrant requirement,” she wrote.

Justice Clarence Thomas objected to “splitting hairs” between breath tests and blood tests. He proposed that neither blood nor breath tests require warrants.

Here is today’s decision.