For decades, bypass surgery, in which surgeons improve blood flow to the heart by sewing new blood vessels to get around blocked ones, was done the same way. The heart was stopped while blood was pumped through a heart-lung machine to do the heart’s work.

But doctors increasingly worried that the machine, the “pump,” might sometimes lead to strokes or memory problems or personality changes. Some privately called patients with those difficulties “pumpheads.”

And so, in the last seven years, many surgeons began offering and patients increasingly demanded an alternative: off-pump surgery in which the machine was not used and doctors operated on a still-beating heart.

Now, a large and rigorous study finds the old way is best.

In the study, published Thursday in the New England Journal of Medicine, 2,203 patients were randomly assigned to have their bypass surgery on pump or off. Because the study was sponsored by the Department of Veterans Affairs, the patients were mostly men.

A year later, those who had had off-pump surgery had poorer outcomes. Fewer bypasses stayed open and patients were more likely to have needed a repeat operation or to have had a heart attack or to have died. They were no less likely to have had strokes or difficulty thinking.

“This is a big one,” said Dr. Eric Peterson, a Duke cardiologist who wrote an editorial accompanying the paper.

“It’s a good study and the fact that it did not find superiority was key,” he added.

Dr. Peterson added that he, like many cardiologists, expected off-pump procedures to be superior.

Dr. Michael Lauer, director of cardiovascular sciences at the National Heart, Lung and Blood Institute, said he anticipated and hoped that the new study would dampen enthusiasm for off-pump surgery.

“Bypass surgery is one of the most common operations in the world,” Dr. Lauer said. “As many as 20 percent of bypasses in the U.S. are being done off pump. This affects a lot of people.”

Dr. Frederick L. Grover, the principal investigator for the study and a heart surgeon at the University of Colorado at Denver and the Denver V.A., said his group was analyzing the costs of the two types of operations. He said if there was a difference, it was slight.

Patients who had their surgery off pump had fewer blood transfusions but spent slightly longer in the operating room. There were no significant differences between the two groups of patients in the time they spent in intensive care after their surgery or how long they spent on a ventilator or how long they spent in the hospital.

Some surgeons who made off-pump surgery their specialty said they were not going to change. The results do not apply to them, they say, because they have extraordinary expertise.

But others less invested in the technique said they would be doing less off-pump surgery. And that includes Dr. Grover.

About 20 percent of the 225,000 to 250,000 people who have bypass surgery each year have it off pump.

Off-pump surgery began to take off around 2002 when instrument makers began selling devices making the surgery seem feasible and animal studies indicated that heart-lung machines had the potential to cause problems.

When they use a heart-lung machine, doctors clamp blood vessels closed, draining the heart of blood. They inject a near-freezing fluid into the heart. They redirect blood through tubes that can create tiny bubbles or small fragments of debris that might get into the brain.

At first, it was not easy to do heart surgery without the pump. How, for example, do you hold part of a beating heart still while you work on it? Some surgeons improvised, using modified kitchen spoons and forks to hold the heart steady. And how do you sew blood vessels onto the back of the heart? Surgeons had to lift the heart to get to the back and then blood pressure would drop.

Instrument makers soon provided special tools that made it easier to steady specific parts of the heart while surgeons worked.

Some, like Dr. Aubrey C. Galloway, who is chairman of the department of cardiothoracic surgery at New York University Langone Medical Center, said he felt compelled to learn off-pump surgery and to do it primarily in high-risk patients.

“There was a lot of market pressure and momentum behind this off-pump stuff,” Dr. Galloway said. “A lot of surgeons were pressured to do it in everyone. Patients were coming in and saying, ‘I’m worried about cognitive dysfunction.’ ”

Now, he said, “the idea that people should go somewhere to get off-pump surgery is pretty much killed by this publication.”

But Dr. Nirav Patel, a heart surgeon at Lenox Hill Hospital in New York, said he does off-pump surgery in 95 percent of his patients and he is not going to change.

He said that even with the new equipment, off-pump surgery was difficult and that it had taken 100 cases before he got really good at it. He estimated that he had now done more than 1,400 off-pump operations and questioned whether the surgeons in the study had the necessary expertise.

“I am an off-pump surgeon,” Dr. Patel said. “I am a big proponent of it.”

It may be, Dr. Lauer said, that surgeons like Dr. Patel are so expert at the procedure that their results are different from those reported in the study.

But, he adds, “from a policy point of view, what we really care about is how well will the procedure work in the hands of a typical surgeon.” The study involved typical patients and typical surgeons. Very few surgeons, Dr. Lauer said, “have achieved exceedingly high levels of expertise.”

And, he added, the study shows that for all the reasoning about why off pump is generally better, “just because something makes sense doesn’t necessarily make it so.”