Ask any company what kinds of benefits its workforce values most, and there’s one that nearly always ranks near the top of the list: Flexibility. It’s prized by both working parents and millennials who crave autonomy, and so employers are under greater pressure than ever to allow staff to work where and when they want. (And, accordingly, to offer the technology that makes it possible.)

So it was surprising to see that a new study found that employers’ idea of flexible work appears to be getting less, well, flexible. The Families and Work Institute and Society for Human Resource Management released the results this week of their 2014 National Study of Employers, an in-depth survey of organizations’ human resources practices and policies.  The study found a noteworthy split in how people viewed employers’ flexibility policies.  When it comes to full-time workers who want control over their schedules, the study found workplaces have grown more accommodating.  In 2014, some 67 percent of organizations allowed employees to occasionally telecommute, up from 50 percent in 2008, the last time researchers asked the question.  There was also an increase in the number of employers who gave staffers control over what time they start and stop work each day.  In 2014, 41 percent of workplaces permitted this, compared to 32 percent in 2008.

But employers are cooling on just about every other form of flexible work arrangement.  In 2008, some 29 percent of companies offered job sharing arrangements; that has fallen to 18 percent.  In 2008, 64 percent of companies allowed employees to take a career break for personal or family responsibilities; in 2014, only 52 percent have such a policy. Wish you could temporarily move to part-time work and keep your job title and your corner office? It’s less likely it’ll be allowed today. This year, 36 percent of organizations say they allow it, compared to 41 percent in 2008.

In other words, it seems employers are more willing to accommodate short-term solutions in which staffers make a minor tweak to their schedules so they can, say, duck out for their daughter’s piano recital or avoid commuting during peak traffic hours. But if you’re seeking more of a schedule overhaul–especially one that would reduce your hours, instead of just reshuffling them–it appears employers are less willing to work with you.

The report’s authors, Kenneth Matos and Ellen Galinsky, write that the sluggish economic recovery might be to blame for the difference. In the downturn and the uncertainty that has followed it, Matos and Galinsky write that the changes “may be a result of employers focusing on maintaining smaller workforces and a reduced emphasis on long-term retention of employees interested in taking extended periods away from work.”

The table below shows the full range of questions FWI and SHRM asked about flexible schedules.

Bottom line?  If you’re thinking about asking for a flexible work arrangement, think wisely about which model you request.