When Steve Good’s two daughters were small, he and his wife Kathleen struggled to handle child-care duties alongside their intense jobs as managers at glass manufacturer Corning Inc. After the second time missing a day-care pickup, the couple decided someone had to take a step back to care for family.

So Mr. Good leaned out, reducing his schedule to 30 hours a week and taking a 25% pay cut. The decision put him in a rare group in the U.S. workforce: professional men who opt to work part time to assist with family duties.

...