Perhaps in the past, high engagement was enough to propel employees to the highest levels of performance. But that’s no longer true, based on the results of an engagement study of 32,000 employees in 29 international markets conducted in 2012 by the consulting firm Towers Watson.

Tony Schwartz, president and CEO of The Energy Project, referenced this study in a blog post earlier this year, When Employee Engagement Turns Into Employee Burnout.

Those stuck on the concept of high engagement might be surprised at these additional findings of the Towers Watson study. “The companies with the highest profit margins had a different employee profile,” Tony wrote. “‘Sustainably engaged’ is the clunky moniker Towers Watson came up with to describe employees who felt their companies energized them by promoting their physical, emotional and social well-being. The top two drivers of performance were having leaders who built trust by demonstrating a sincere interest in employee well-being and having manageable stress levels, with a reasonable balance between work and personal life.”

In other words, those go-go-go super-employees who are chronically gung-ho and work 60+ hours a week? Their extremely high levels of performance and extremely high levels of stress are unsustainable, and they are at great risk for burn out.

The good news, Tony reports: “Companies in which employees reported feeling well taken care of — including not working too many hours — had twice the operating profit margins of those with traditionally engaged employees, and three times the profit levels of those with the least engaged employees.”

So what’s the elephant in the office? All over the world, Tony says, employees are running on fumes. Exhausted. Stressed out. Too many are dying prematurely from heart attacks, and there are incidents of leaders committing suicide.

Rather than measure the engagement level of employees, Tony suggests, measure how consistently energized they feel. “That means focusing not just on inspiring them and giving them opportunities to truly add value in the world, but also on caring for them and providing sufficient time to rest and refuel,” he says.

The post ends with this powerful statement: “No chief executives of any large company that I’m aware of have truly stepped up to use their bully pulpit to be a model and spokesperson for a balanced life — meaning not just offering perks like meditation classes, but a culture that truly meets people’s multidimensional needs. That’s what we need now, more than ever — chief executives truly willing to make the care of people the highest priority, beginning with themselves. Who will be the first?”