The New York Times has one million digital subscribers, but it wants more. Now it looks like it’s trying to get them by plugging holes in its paywall.

The Times is experimenting with limiting the number of stories that Facebook and Twitter users can read each month without paying for a subscription.

Two months ago, the Times began capping some Facebook users’ access to the site at 10 articles a month, said NYT rep Eileen Murphy. On Friday, she said, the NYT expanded the test limits to referrals from Twitter and other services.

When the Times first launched its subscription service in 2011, it restricted the number of stories readers could consume on the Web without subscribing, (first to 20 per month, then 10), but let users who got to the paper via a Facebook or Twitter link read as many stories as they wanted.

The notion behind the “leaky paywall” was obvious — the NYT was hoping that the social networks would help expose the paper to people who didn’t see it very often.

But that was five years ago, and now it looks as though the NYT wants to convert some of those social browsers into paying customers. Murphy says the new limit “impacts about 50 percent of readers who have read more than 10 articles per month,” and it’s possible that the paper will decide to abandon the test at some point.

But my hunch is that we’ll continue to see paywalls get harder to scale, even as publishers work harder to find new readers/subscribers. The Wall Street Journal, for instance, is now giving away some of its stories via a Snapchat Discover channel, but has also moved to make it harder to read WSJ stories via a Google search back door.

The Times, meanwhile, was one of the first publishers to work with Facebook’s “Instant Articles” format, which publishes entire stories on the social network that anyone can read for free. But unlike the Washington Post and other publishers, the NYT is only publishing a selection of its stories in that format.