In February 2012, David Rubincam, the FBI’s legal attache in Moscow, escorted a group of Russian security officials to observe security arrangements at Super Bowl XLVI in Indianapolis.

The delegation from the Federal Security Services, known as the FSB, wondered why the stadium wasn’t brimming with armed troops. It also hadn’t occurred to the Russians that private security firms working for the event’s sponsors had been integrated into the overall counterterrorism effort.

They were surprised “by some things that were really kind of eye-openers,” said Rubincam, who explained to the five senior officers that “we have tons of security in place, but the participants don’t see it. That’s what you want.”

Rubincam hopes the lessons the Russians learned at the Super Bowl will help make the Winter Olympics in Sochi safer. But he’s not sure, and neither are some other current and former U.S. security officials.

Although the Russians are relying on a show of force at the Games, deploying 40,000 heavily armed police and other security officials to the area, the security risks are regarded as unusually high compared with past Olympics. The main threat emanates from Islamic radicals who are based in the nearby Caucasus and who have vowed to launch attacks during the event.

Last month, suicide bombers struck twice in the city of Volgograd, killing 34 people and injuring scores at a train station and on a moving bus. Fears were heightened this week when Russian security officials asked for the public’s help to locate a female suicide bomber who may already be in Sochi.

The U.S. State Department has issued an advisory for Americans traveling to the Olympics, which open Feb. 7. Thousands of Americans are expected to attend.

White House spokesman Jay Carney said Thursday that U.S. officials had seen an “uptick in threat-reporting prior to the Olympics” but added that it was not unusual to see such a rise ahead of a major international event. Lisa Monaco, President Obama’s counterterrorism adviser, is leading an interagency panel to coordinate U.S. support for the Games.

Rubincam, who served as the FBI’s top representative in Moscow from May 2011 to October 2012, said the Russians have been reluctant to accept American aid in securing Sochi and are suspicious of the offers of assistance.

Former FBI agent Jim Treacy, who also worked in Moscow as a legal attache, said the Russians would be “equally concerned as our folks being involved in intelligence-gathering while doing security and counterterrorism.”

Rubincam said that by September 2011, he had started trying to work with the Russians in planning for Sochi. The discussions were complicated by larger diplomatic strains in the relationship that only deepened after Vladi­mir Putin returned to the presidency in 2012.

“When I got there, the cooperation on terrorism had fallen to zero,” Rubincam said. The limits of the relationship were highlighted by the Boston Marathon bombing, after which U.S. and Russian officials blamed each other for not following through on leads that might have identified two ethnic Chechen brothers before they were implicated in carrying out the attack.

The United States offered to send as many as 100 personnel to Sochi, including the FBI’s highly regarded bomb technicians. Rubincam said the FBI had a laundry list of capabilities that the FBI’s Critical Incident Response Group could bring to bear. The Russians refused, he said, and countered that the United States could dispatch up to a dozen or so security officers.

“What they came back with was a fraction of what we offered,” said Rubincam, who visited Sochi twice.

The message was clear, Rubincam recalled: “You can show up, but you’re just going to be window dressing.”

In the end, the FBI settled on sending a few dozen agents to Russia. Some will operate out of the U.S. Embassy in Moscow, where they can handle classified information securely. Others will be on the ground at a shared facility in Sochi. Agents will be unarmed. The FBI will also work closely with the State Department’s Bureau of Diplomatic Security service.

In comparison, for the Athens Games in 2004, the FBI sent 150 agents and the Defense Department positioned an aircraft carrier off the coast, said Raymond Mey, a former FBI agent and deputy on-scene commander at the time. The Pentagon has said it will place two warships in the Black Sea during the Sochi Games, in case it needs to evacuate Americans.

Putin faces a “daunting task,” said Mey, who first helped plan security at the Olympics, in Atlanta in 1996.

Mey said that although the Russians will be able to control access to official venues, he worried about soft targets. Islamic terrorists from the region have previously attacked a Moscow theater, the city’s subway system, a rock concert, airliners and a school in the town of Beslan, a siege that ended in the deaths of 380 people, including many children.

“It’s going to be hit or miss whether they’re able to stop this or not,” Mey said, referring to suicide bombers.

Mey recalled the precautions he took at the Olympics in Salt Lake City in 2002, just months after the Sept. 11, 2001, terrorist attacks. He dispatched 200 two-man surveillance teams to focus on potential targets, including lines leading to venues.

Rubincam said U.S. security assessments of Sochi are not “rosy.” He declined to provide details because the information was classified.

On Thursday, Rep. Michael McCaul (R-Tex.), who chairs the House Committee on Homeland Security and who recently returned from a trip to Sochi, said that intelligence-sharing between the United States and Russia about internal threats could be better and that he had serious concerns about a possible attack.

“They’re loathe to share” information, he said.

McCaul added, however, that the Russians had established a ring of steel around Sochi in attempt to thwart any threat. He also said Putin appeared to be doing all he could to secure Sochi.

“Everything is on the line. He knows that,” McCaul said.