A new survey from the Centers for Disease Control and Prevention finds that 41% of American homes are mobile phone only. That number is on the rise, but not climbing nearly as fast as it once was. Landline cord cutting seems to be at a plateau.

“For most of the past decade, the rate has been increasing by 4 or 5 percentage points,” explains Stephen Blumberg, lead author of the report from the CDC’s National Center for Health Statistics. “In the past year, that rate of increase has slowed. The increase was only 2.8 percentage points.”

Nobody is predicting a landline renaissance. Weston Henderek, who tracks wireless use for market research firm Current Analysis, thinks cord-cutting will march on, but probably not as fast as it had been going.

“We’ve picked all the low-hanging fruit, if you will,” Henderek says. “A large percentage of the people that wanted to cut the cord already have.”

It’s not just nostalgia that keeps some people hanging on. Many homes need a landline because of poor cell phone reception in their area. Others have home phones bundled with their cable and Internet packages.

Even some mobile phone analysts still have landlines. Alongside some 15 mobile phones in his home, Henderek has a trusty old landline. His home security system requires it.