During the 2007-8 financial crisis, Chris Reining said, he panicked. His state of anxiety wasn’t brought on by the collapse of the United States stock market or the global economic crisis that followed. It was prompted by his office mates in Madison, Wis.

“I was living the 9-to-5 life, and I would look at other people at work and see that they were 30, 40 years older than me and still living the cubicle lifestyle,” Mr. Reining, 36, said of his 29-year-old self. “I didn’t want to be living that life. It was this feeling of being trapped and not being in control, being enslaved to a job, being enslaved to my possessions.”

Unlike the crisis of a milestone birthday, where fear subsides into resignation, Mr. Reining decided to change his cubicle fate and set a goal of having $1 million in his brokerage account by the time he was 35. Given that he was making about $75,000 a year working in information technology, he knew the goal would take considerable discipline.

Mr. Reining is part of a small group of supersavers who commit to a number that they say will support their lifestyle in retirement and never stray from achieving that goal. They are the financial equivalent of people who go on a diet, lose the weight and actually keep it off.