College graduates who took a detour around the weak job market by going back for advanced degrees are beginning to emerge from those programs—and finding job prospects aren't much better than they were a couple of years ago.

The jobless rate for 20- to 34-year-olds with master's degrees, though well below the overall 9.5% U.S. average, was 4.2% in June, the Labor Department said Friday, up from 3.9% last year and 2.9% in June 2007, before the recession started.

The economy has started creating jobs—albeit at a slow rate—in recent months. But those with new master's degrees often aren't at the front of the line to get them, say experts. One reason: They frequently compete for jobs that require those advanced degrees with older workers who have the advantage of more work experience.

Caitlin Johnson, 23 years old, may soon find herself among them. A 2009 graduate of Massachusetts Institute of Technology with a B.S. in computer-science and engineering, she said she was unable to land any of the 10 positions she applied for.

So she opted to stay at MIT for her master's in engineering. Having just finished her first year of the two-year program, Ms. Johnson said she might look for a job at the end of the summer to start after she completes the degree next year. But finding graduate school more appealing and facing a job market that remains weak, she said she would most likely go on to earn her Ph.D.