With waves of retirement-age employees on their staffs heading for the exits, senior leaders in government are getting worried that the generation of millennials in line behind them are hard to attract and even harder to keep.

The officials seem to have good cause for concern: The share of the federal workforce under the age of 30 dropped to 7 percent this year, the lowest figure in nearly a decade, government figures show. Overall, about a third of the private-sector labor force was born between 1980 and 1995, but younger workers make up only a quarter of federal, state and local government employees.

For several years, government surveys and outside studies have concluded that the foundation of millennials at all levels of government is shrinking because young people don’t view public service as a permanent career the way older generations did.

But a new study out Tuesday from Deloitte Consulting debunks many of these assumptions, concluding that the picture for millennials in government is actually a lot brighter than anyone thought.

Deloitte decided to question some of the conclusions of its own inquiry on the subject, done last year with the nonprofit Partnership for Public Service. It showed the number of federal employees under 30 at their lowest levels since 2005, dropping by more than 45,000 people since 2010.

“We wanted to go out and say, ‘Is that really true?'” said Sean Morris, director of Deloitte’s Federal Human Capital Practice. “Does the data actually say young people are less passionate about jobs in government, or they won’t stick around for long? What it looks like is more positive than what people generally think.”

The new study looked at data from U.S. Census Bureau on the public sector workforce and the National Opinion Research Council at the University of Chicago. Here are four myths the report debunks about the youngest public servants at the federal, state and local levels:

1. They have higher turnover rates than older generations.

The studies that support this view are often based on tenure — how long employees have held their jobs — rather than true turnover rates, Deloitte found. But the tenure measure is a problem, since millennials tend to go into government at older ages than previous generations.

The state and local government turnover rate for 25 to 34 year-old employees was approximately 5 percent in 2006, but declined to less than 3 percent in 2013, the study found.

2. They’re less passionate than older workers about their jobs in government.

The Office of Personnel Management’s annual survey of federal workers shows that millennials have the same morale as older workers, and in recent years it’s been low. But young people in government are not distinguished by worse morale than anyone else.

3. They don’t stick around — they’ll decamp to the private sector in a heartbeat.

Various experts have sounded this alarm, Deloitte says, but the data doesn’t bear it out. It shows a decline in government workers age 20-35 who plan to look for work in the coming year.

Millennials do like public service. But obstacles get in the way of government keeping them for at least a chunk of their careers, chief among them the slow hiring process.

4. It’s harder to recruit them for public service than previous generations.

The study says there’s no conclusive answer to this right now. Hiring officials worry that millennials are harder to recruit because they have so many options at nonprofits and private companies. But the number of students getting degrees in public administration is up.

A tightening labor market after the Great Recession has made it easier for young people to be choosier about jobs, the report says. The supply of millennials entering government is not keeping up with older generations. But part of the problem is that government is hiring less overall. And partly because of this slump, recruiting for public sector jobs is slipping. “We’ll have to say that the jury is still out on the difficulty of recruiting millennials into government jobs,” the study concluded.

It makes a few recommendations, including that that government agencies tailor benefits to millennials as a recruiting tool, offering student loan payment assistance, for example. It also suggests that government focus less on generational differences and more on offering benefits that appeal to both younger and older workers, like a range of health insurance plans.