All that did was impel the group to dig in. Finally, on April 19, the F.B.I. mounted a full assault, pumping in large quantities of military-grade tear gas. Fires, which independent investigators later deemed to have been set by the Davidians, engulfed the compound. Shooting could be heard inside. When it was all over, 75 people were dead, a third of them children. Some, including Mr. Koresh, had been shot by fellow sect members. There were few survivors.

The Waco events did not occur in a vacuum. Eight months earlier, federal agents laid siege to the compound of a family of white separatists in Ruby Ridge, Idaho. That encirclement also ended badly, with several people killed, among them a 14-year-old boy. F.B.I. officials later acknowledged that their operations at Ruby Ridge had been “terribly flawed.”

As for Waco, a Harvard professor of law and psychiatry, Dr. Alan A. Stone, took the F.B.I. to task in a report to the Justice Department in November 1993. An apocalyptic sect like the Branch Davidians should not have been handled as if it would “submit to tactical pressure” the way a band of ordinary criminals would, Dr. Stone said. Government agents sought to prove to Mr. Koresh that they were in control. Instead, Dr. Stone said, they drove him to the “ultimate act of control — destruction of himself and his group.”

The grim events in Texas and Idaho proved sobering for the government. Its agents began to exercise more patience with defiant militant groups. An armed standoff in 1996 with the Montana Freemen ended without a shot fired and with the Freemen’s surrender after 81 days. In Nevada last year, agents of the federal Bureau of Land Management tactically retreated rather than get into a shooting war with rifle-toting supporters of Cliven Bundy. Mr. Bundy, a rancher given to racist rants, owed the government more than $1 million in grazing fees amassed over two decades, but cast his refusal to pay as the act of a patriot and not, as many of his critics suspected, of a deadbeat.

Throughout, the specter of Waco has not faded. Right-wing extremists regularly invoke it as a defining moment, proof of Washington’s perfidy. “Waco can happen at any given time,” Mike Vanderboegh, a prominent figure in the Patriot movement, told Retro Report. He added ominously: “But the outcome will be different this time. Of that I can assure you.”

One man who took the notion of a different outcome to a murderous extreme was Timothy J. McVeigh, who went to Mount Carmel and observed the siege. On April 19, 1995, two years to the day after the mass deaths there, he and an accomplice, Terry L. Nichols, bombed a federal building in Oklahoma City, killing 168 people and wounding nearly 700 others. It was the most devastating act of domestic terrorism in American history. Mr. Nichols was sentenced to life in prison, Mr. McVeigh to death.

Interviewed in prison by two Buffalo News reporters in 2001, the year he was executed, Mr. McVeigh said: “Waco started this war. Hopefully, Oklahoma would end it. The only way they’re going to feel something, the only way they’re going to get the message is, quote, with a body count.”