When a law has a name like “Patriot” or “Freedom,” it’s a sign that you should read the fine print. Somewhere down there, in the terraced subclauses of some forgettable subsection, is a word with a special meaning, a word that offers shelter and concealment to whatever it is that the law actually does. Consider the word “relevant.” You and I use the word to distinguish what matters (the relevant) from what does not (the irrelevant). But to the National Security Agency, there was no irrelevant. Pointing to one appearance of the word in a 2006 update of the USA Patriot Act, the agency argued it could demand records of any one of our phone calls, on the very slight chance of some distant connection to terrorism. A secret court agreed, ordering phone companies to serve up our records on an “ongoing daily basis’’ — 24 hours a day, hundreds of billions of calls in all. No one knew about it until Edward Snowden revealed the existence of the program in 2013. Earlier this month, President Obama signed the USA Freedom Act, which is supposed to close this loophole. Will it? That depends on a fresh pile of fine print.

Congress created the ‘relevant’ loophole soon after it learned of an even larger loophole: the free-for-all surveillance program put in place after the Sept. 11 attacks. At first, N.S.A. dragnet surveillance was so secret that it didn’t really have a name. It was simply known as ‘‘the Program’’ or ‘‘the President’s Surveillance Program’’ and later as ‘‘the Terrorist Surveillance Program’’ or by the cover term ‘‘Stellarwind.’’ As reported by the journalist Shane Harris in his book ‘‘The Watchers,’’ the N.S.A.’s data scientists came to call it ‘‘the Big-Ass Graph’’ for its tendency to generate ‘‘hairballs,’’ knotted webs of associations that rarely added up to anything. The graph began with phone ‘‘metadata’’ from Verizon and other U.S. carriers — whom their customers called, where they called from and for how long they talked. It also included Internet metadata, compelled from Silicon Valley firms, as well as data from hotels, car-rental companies, airlines and banks. In thousands of cases, it went beyond metadata to obtain the wiretapped content of phone calls or emails.

In 2004, the White House began to hand its self-arrogated surveillance powers over to the Foreign Intelligence Surveillance Act court, a secret tribunal created in 1978 to oversee wiretaps. After The New York Times published a 2005 exposé of the Program, which it called ‘‘warrantless wiretapping,’’ Congress got involved. Like a tray of ice cubes, the Program was broken up and tucked into various amendments of the 1978 FISA law. Content from overseas Internet and phone taps went into Section 702. Internet metadata went into Section 402. Phone metadata went into Section 501, formally known as 50 U.S. Code § 1861, more commonly known as Section 215, after the section of the Patriot Act that amended it.

The original version of Section 215 allowed the F.B.I. to gather records (including phone records) from businesses (like phone companies) under the supervision of the secret FISA court. For the court to grant an order, the F.B.I. had to show:

… that the records concerned are sought for an authorized investigation …

But this passage changed in the law’s new incarnation. Now the F.B.I. had to show:

… there are reasonable grounds to believe that the tangible things sought are relevant to an authorized investigation …